From a Trinitarian perspective, does the term 'only begotten Son' make sense outside of the concept of the incarnation?

Aquinas addresses the question from different angles a number of places in the Summa Theologica, in various parts of the "Treatise on the Most Holy Trinity" (First Part, Questions 27–43).
The fundamental question is answered more or less directly in Question 27, "The Procession of the Divine Persons". Article 2 of this question, "Whether any procession in God can be called generation?", talks about what it might mean to say that the Son "is begotten by" the Father. Thomas' answer is:

... We must observe that generation has a twofold meaning: one common to everything subject to generation and corruption; in which sense generation is nothing but change from non-existence to existence. In another sense it is proper and belongs to living things; in which sense it signifies the origin of a living being from a conjoined living principle; and this is properly called birth.
Not everything of that kind, however, is called begotten; but, strictly speaking, only what proceeds by way of similitude. ... the procession of the Word in God is generation; for He proceeds by way of intelligible action, which is a vital operation:—from a conjoined principle (as above described):—by way of similitude, inasmuch as the concept of the intellect is a likeness of the object conceived:—and exists in the same nature, because in God the act of understanding and His existence are the same, as shown above. Hence the procession of the Word in God is called generation; and the Word Himself proceeding is called the Son.

The Son, in other words, is "begotten" not in virtue of the Incarnation, but because the Son is the Word of God proceeding from, and in that sense "begotten by" (one could say "generated by"), the Father.
There are a few other places where Aquinas discusses different aspects of the question (such as "Is it appropriate to call the Father 'unbegotten'?"), but this is the clearest exposition of Aquinas' actual position, and it appears from his discussions as a whole to be a standard Trinitarian answer.


Which Christian denominations do NOT believe that Jesus existed prior to his conception?

Iglesia ni Cristo (Church of Christ) has ~2.3 million adherents and is the 3rd largest religious group in the Philippines.

"But we do not subscribe to the belief that Christ is a God-Man or
both God and man. He is man in nature according to His own testimony
(John 8:40) and the teachings of His Apostles (I Tim. 2:5; Matt.
1:18)." The Lord Jesus Christ

More specifically, a letter to the editor of Iglesia ni Cristo's publication God's Message asked

"Why is it that your  religion does not teach these three basic
doctrines (divinity, pre-existence, incarnation) about Christ?"

and the answer was in part

"What is spoken of in John 1:1, 14 as being with God in the beginning
is the "Word." Hence, in order to understand the real message of John
1:1, 14, we should first clarify the meaning of the term "Word." Does
it  really  refer to a 'pre-existent Christ' as others allege? No.
The Holy  Scriptures prove instead that the "Word"  refers to God's
"promise" to send His  Son, which He "announced" before[.]"

Christadelphians number ~60,000 adherents.

"Jesus Christ is a man, Christadelphians say, not God. He did not
exist prior to his earthly incarnation." Christadelphian beliefs and
practices

Church of God, General Conference has ~5,000 adherents.

"Jesus is the Christ. Existing from his mother’s womb, he is the
virgin born son of God (Luke 1:34-35, Gal. 4:4)." Our Beliefs

I'm sure there are more, but verifying non-English churches becomes tricky.
BiblicalUnitarian.com and the Revised English Version Bible translation (including commentary and appendices) is by the Spirit and Truth Fellowship, a non-denominational ministry. I do not know the number of people affiliated with the organization (I presume it is small), but the resources they provide seem the most comprehensive and easily accessible of Biblical Unitarian groups. They hold that Jesus pre-existed only in the sense of being part of God's plan. I believe this would qualify them as denying Jesus' pre-existence per the OP.

"The Jewish worldview was that something planned (that is, foreknown
in the counsel of God) existed notionally or ideally, but not yet in
actuality upon earth in our experience. [...] When this paradigm is
applied to those texts which seem to our Western understanding to
imply that Jesus personally did consciously exist (as God) before his
physical appearance on earth, confusion disappears." Jesus'
Pre-Existence - Literal or Ideal?

Christian Science (Church of Christ, Scientist) has ~100,000-400,000 adherents, and might seem to qualify as it holds Jesus is a man.

"Jesus Christ is not God, as Jesus himself declared [...] Jesus is the
name of the man who, more than all other men, has presented Christ,
the true idea of God[.]" Christian Science Beliefs quoting
Science and Health by Mary Baker Eddy

Christian Science isn't a creedal denomination (see here), but the founder Mary Baker Eddy held to universal pre-existence in some sense, referring to "man's spiritual preexistence as God's child". As the article continues, commenting on this:

"Christian Science teaches that man's identity, his real being, is the
reflection of Spirit, and therefore wholly spiritual, and that his
existence as the child of God, who has existed with his Father-Mother
God "from the foundation of the world," is eternal.

According to Christian Science, when Jesus said "Before Abraham was, I am" the 'I am' was referring to a universal Christ of man's true spiritual nature.

"When Christ Jesus made the startling declaration, "Before Abraham
was, I am," he not only referred to the eternality of universal Truth,
but also to his own pre-existence as the individual son of God, an
individual instance of divine reflection. It will be readily seen that
these words apply to all the individual sons of God, just as they did
to Jesus, the Christ." Before Abraham Was

So, it seems this denomination believes Jesus pre-existed, as all humans have in their 'real being'.


Why is it said that the Gospel of Matthew presents Jesus as the King of the Jews?

The Gospel of Matthew is written for a Jewish audience, especially Palestinian Jews who were at the time oppressed by the Romans. One of Matthew's main goals in his gospel was to prove that Jesus was the true Davidic Messiah--the king the Jews were expecting, who will deliver them from oppression.

Jewish scripture foretold that the Messiah will be like a Star out of Jacob and the Scepter that rises out of Israel in Numbers 24:17. He is the One who sits on David’s throne in Isaiah 9:7. He comes with the clouds of heaven to reign over a kingdom where all people, nations, and languages, will serve Him in Daniel 7:13-14. In His kingdom the nations will no longer lift up the sword against one another in Isaiah 2:4, and His reign, we’re promised, will have no end in Isaiah 9:6-7.

And hence Jesus Christ is presented as the “Son of David, the Son of Abraham” in Matthew 1:1 and the “King of the Jews” who wise men seek to worship in Matthew 2:2. Forty times He speaks of the kingdom of heaven and says that the day would come when He would return in the clouds to establish His kingdom on earth in Matthew 26:64.

Even Jesus is presented being asked directly, “Are you the King of the Jews?” to which He replies, “I am” in Matthew 27:11. This infuriated the religious leaders who demanded He be crucified. As He hung on the cross a sign was put over His head that read, “This Is Jesus, The King Of The Jews.”


Is the idea that the pleasures we experience now are mild foretastes of Heaven Biblical?

There are many ways of coming at your question.  In somewhat random order, I suggest the following as answers:

Why do you think another word for heaven is paradise?  Is it because its joys are fewer and less intense than the joys on earth?  There's an ironic phrase that goes "trouble in paradise," which is ironic simply because there is no trouble in paradise!  See Paul's description of what he heard in the "third heaven," which he also called paradise (2 Cor 12:1 ff.).
How could heaven not be better than the best that life has to offer here on earth, since in heaven there will none of the following:  tears, death, mourning, crying, pain (Rev 21:4); the old things (Rev 21:5); thirst (Rev 21:6); ugliness (look at Revelation 21 and its description of the holy city, New Jerusalem); dogs, sorcerers, immoral persons, murderers, idolaters, liars (Rev 22:15); darkness (Rev 21:23); Satan and his demons (Rev 20:10)
How about the positive things heaven has to offer:  the presence of Jesus (1 Thes 4:17); perfect, complete, face-to-face knowledge, and not the knowledge of imperfect reflections as in a mirror (1 Cor 13:10-13); eternal life (John 3:16); all of God's saints from time immemorial to saints whom we knew on earth as family members, friends, acquaintances, mentors (1 Thes 4:13-18, and Revelation, passim); the worship of God without the distractions of sin, time limitations, unanswered questions, trials and tribulations, and a host of factors that cause our fellowship with other believers to be less than joyful here on earth, such as: divisions according to sex, denomination, skin color, national origin, language, culture, customs, appearance in general, in-groups and out-groups, cliques, theological differences, age, and so much more.

I could go on for quite a bit, but I think you get the idea.  I haven't even dipped into the hints of eternal bliss that are found in the Old Testament, and I'm sure there are many.  Maybe I'll revise my answer another time!


Where in the Bible does it say we have a sin nature?

The phrase " sin nature " is not used in the bible I use, KJV. However, there are verses that imply such.

Psalms 51;5
 Behold,I was shapen in iniquity,and in sin did my mother conceive me.

Psalms 58;3
The wicked are estranged from the womb:they go astray as soon as they be born, speaking lies.

Ephesians 2;3
Among whom also we all had our conversation in times past in the lusts of our flesh, fulfilling the desires of the flesh and of the mind; and were by nature the children of wrath, even as others.

We are all children of wrath until we are born again, John 3;5.


Does the Catholic Church teach that the Catholic faith is demonstrably true?

No, not all the truths of the faith are demonstrable.
First Vatican Council, Dei Filius IV canon 1 on faith & reason:

If any one shall say that in divine revelation there are no mysteries, truly and properly so called, but that all the doctrines of faith can be understood and demonstrated from natural principles, by properly cultivated reason: let him be anathema.[Cdl. Manning's transl. of:] Si quis dixerit, in revelatione divina nulla vera et proprie dicta mysteria contineri, sed universa fidei dogmata posse per rationem rite excultam e naturalibus principiis intelligi et demonstrari: anathema sit.

Some truths of the faith cannot be demonstrated, such as the Trinity, although they can be shown not to be contrary to human reason. St. Thomas Aquinas, the greatest Doctor of the Church, said in his Summa Theologica I q. 32 a. 1 c.:

It is impossible to attain to the knowledge of the divine persons of the Trinity by natural reason.
impossibile est per rationem naturalem ad cognitionem Trinitatis divinarum personarum pervenire.

Thus, faith is necessary to understand "what belongs to the distinction of the persons," St. Thomas continues, and "by natural reason we can [only] know what belongs to the unity of the essence [of God]."
See the first chapters of St. Thomas's Summa contra Gentiles book 1, esp. these:

On the way in which divine truth is to be made known
That the truth about God to which the natural reason reaches is fittingly proposed to men for belief
That the truths the human reason is not able to investigate are fittingly proposed to men for belief
That to give assent to the truths of faith is not foolishness even though they are above reason
That the truth of reason is not opposed to the truth of the Christian faith
How the human reason is related to the truth of faith

Even Aristotle realized that not all truths are demonstrable.


Has the Roman Catholic Church ever issued an official response to the accusations of the Reformers?

The only response I know of it the counter-reformation amount the Catholics : http://en.wikipedia.org/wiki/Counter-Reformation.

period of Catholic revival beginning with the Council of Trent (1545–1563) and ending at the close of the Thirty Years' War, 1648 which is sometimes considered a response to the Protestant Reformation. The Counter-Reformation was a comprehensive effort, composed of four major elements:

Ecclesiastical or structural reconfiguration
Religious orders
Spiritual movements
Political dimensions


Let us leave aside the age of Jacob, it is possible to deduce the a number of other facts about his chronology.

Following his deception of Esau, Jacob left Beersheba (Gen 28:9) and went to Paddan-aram (Gen 29) and worked for his uncle Laban for 7 years (Gen 29:20) for the hand of Rachel but ended up having to marry Leah as well as Rachel (v27).  As a result, he had to work for another 7 years (v30) for the second wife as well.
Gen 30 describes the birth of the first 11 sons (and 1 daughter, Dinah) of Jacob born in the that second 7 year period.  It was at the end of the second seven year period that Joseph was born (Gen 30:25ff) and that Jacob wanted to leave but was persuaded to stay longer.
Jacob worked a total of 20 years for Laban (Gen 31:38).  At the end of this, Joseph is 6 years old.
At the end of 20 years, Jacob had to deceive Laban (Gen 31:20) and flee for his life and left to return to Beersheba but actually settled in Shechem (Gen 33:18).  At this point, Joseph was the youngest son (Gen 33:2) and the only child of Rachel.
An unknown time later, he moved to Bethel (Gen 35:1).  (This must have been at least 1 year later.)
Later still, the moved to Ephrath (Gen 35:16).  This must have been at least 1 year later.)  It was during the move to Ephrath that Benjamin was born and Rachel died.  This means that it was a minimum of 13 years in Paddan-aram plus at least 2 more years that Jacob was married to Rachel.  That is a minimum of 15 years.  Joseph at this point must have been at least 8 years old.
We also know that by the time Joseph was 17 years old (Gen 37:2) his mother had been dead for some unknown time before.  This was 11 years after leaving Paddan-aram.  If Rachel died just (say) two years before Joseph was 17, that is at the age of (say) 15, then Jacob and Rachel would have been married for 13 years in Paddan-aram plus another 9 years, a total of no more than 22 years.

All this means that Jacob was married to Rachel for some time between about 15 years and 22 years.  The uncertainty arises from the unknown time between Jacob leaving Paddan-aram and arriving in Ephrath which was presumably at least 2 years (with Bethel in between) and when Joseph was 17 years old.

My best guess (that is all) is that they were married for about 18 years on the basis that it was about 5 years between Paddan-aram and Ephrath and about 6 years before Joseph's 17 birthday.  [That is Joseph was about 11 years old when Rachel died??]  But that is a guess.


Is there any evidence to support the claim that the Apostle St. Peter founded the Church in Antioch and, if so, what are the implications?

Interesting question akin to did Peter found the church at Rome.  Historical evidence of either is scant, but here is Eusebius and Schaff's commentary.  For Eusebius, Evodius was first bishop, followed by Ignatius.

  At this time Ignatius was known as the second bishop of Antioch, Evodius having been the first.
  -source-

And commentary:

  738    We cannot doubt that the earliest tradition made Evodius first bishop of Antioch, for otherwise we could not explain the insertion of his name before the great name of Ignatius. The tendency would be, of course, to connect Ignatius directly with the apostles, and to make him the first bishop. This tendency is seen in Athanasius and Chrysostom, who do not mention Evodius at all; also in the Apost. Const. VII. 46, where, however, it is said that Evodius was ordained by Peter, and Ignatius by Paul (as in the parallel case of Clement of Rome). The fact that the name of Evodius appears here shows that the tradition that he was the first bishop seemed to the author too old and too strong to be set aside. Origen (in Luc. Hom. VI.) is an indirect witness to the episcopacy of Evodius, since he makes Ignatius the second, and not the first, bishop of Antioch. As to the respective dates of the early bishops of Antioch, we know nothing certain. On their chronology, see Harnack, Die Zeit des Ignatius, and cf. Salmon’s article Evodius, in Smith and Wace’s Dict. of Christ. Biog.
  -ibid-

So, according to the Apostolic Constitutions Book VII P 46, the claim is that Evodius was first bishop, but who was appointed as such by Peter.

  Of Antioch, Euodius [Evodius], ordained by me Peter; and Ignatius by Paul.
  -source-

The sense is not necessarily that Peter lived for years in Antioch, but rather visited and established his successor Evodius, the first bishop.

Implications of this tradition of Peter founding the church at Antioch?  It depends on one's interpretation of the well discussed "upon this rock" being either Peter or his confession.  If one believes the rock refers to Peter, then we have competing claims as to which church that might be; that is, either the one sourcing to Antioch or Rome or even Jerusalem.  If one believes the rock refers to one's confession of faith in Christ, then it basically does not matter the location of where Peter roamed, but rather just the facts that he and the other apostles did carry the gospel, the good news, message outward from Jerusalem to the ends of the earth.


Is there no salvation among any Christ-professing faiths, apart from the restored gospel of the Latter Day Saints? (LDS perspective)

“Salvation” and “saved” are used in the scriptures in multiple contexts with several different meanings.
In one context, all of God's children will receive Salvation from Physical Death. Whether they are LDS, of some other Christ-professing faith, or any other faith - including atheists. Every person born to earth has kept their first estate, will be resurrected, and will live on the Earth after it has received it's paradisiacal glory†. We were saved before we were born, our births are a testament of this, we have all been saved from physical death.
In another context, there is Salvation from Sin. To be cleansed from sin through the Savior's Atonement, an individual must exercise faith in Jesus Christ, repent, be baptized, and receive the gift of the Holy Ghost (see Acts 2:37-38). This is only possible through membership in Christ's restored church, which is the Church that bears his name and his priesthood, the Church of Jesus Christ of Latter-day Saints.
Christ revealed to the Prophet Joseph Smith in 1820 that not one Church on earth had the proper priesthood authority to baptize in his name, that the priesthood had been lost during the great apostasy. That authority was restored through Joseph Smith, and the restored Church is the only church through which a man can be baptized and receive Salvation from Sin.

What is meant by "first estate" and "second estate"?
It's the difference between Salvation, and Exaltation.
To be brief, we all lived as spirits in the presence of God as Spirits before the creation of the Earth. We refer to this time as the preexistence. When God presented the plan of salvation there were two who offered to fulfill the role of Saviour on earth. The first was Jesus Christ, the second was Lucifer. They presented their plans for redeeming mankind and The Father chose Christ's plan over Lucifer's. Lucifer was angry, rebelled against God, and led many spirits away when God cast him out of his presence (see Abraham 3:22-28). Those who chose to stay and accept Christ's plan where those who kept their first estate, and would be privileged to be born on earth, receive a physical body, and be resurrected. Those who followed Lucifer (Satan) did not keep their first estate, and shall remain as spirits forever and dwell in eternal darkness after the earth has received it's paradisiacal glory.
Those who have kept their first estate have been born on earth or will be born someday and face the trials of mortality. Those who are baptized and have receive the Holy Ghost through the proper priesthood authority are conditionally saved from sin. In this sense, salvation is conditional, depending on an individual's continuing in faithfulness, or enduring to the end in keeping the commandments of God, also referred to as keeping their second estate. Those who keep their second estate shall receive Exaltation, and be exalted with our Saviour Jesus Christ and our Father in Heaven.

Abraham 3:22-28
22 Now the Lord had shown unto me, Abraham, the intelligences that
were organized before the world was; and among all these there were
many of the noble and great ones;
23 And God saw these souls that they were good, and he stood in the
midst of them, and he said: These I will make my rulers; for he stood
among those that were spirits, and he saw that they were good; and he
said unto me: Abraham, thou art one of them; thou wast chosen before
thou wast born.
24 And there stood one among them that was like unto God, and he said
unto those who were with him: We will go down, for there is space
there, and we will take of these materials, and we will make an earth
whereon these may dwell;
25 And we will prove them herewith, to see if they will do all things
whatsoever the Lord their God shall command them;
26 And they who keep their first estate shall be added upon; and they
who keep not their first estate shall not have glory in the same
kingdom with those who keep their first estate; and they who keep
their second estate shall have glory added upon their heads for ever
and ever.
27 And the Lord said: Whom shall I send? And one answered like unto
the Son of Man: Here am I, send me. And another answered and said:
Here am I, send me. And the Lord said: I will send the first.
28 And the second was angry, and kept not his first estate; and, at
that day, many followed after him.

† There are few exceptions who will not live on earth, but instead will be cast out to dwell in outer darkness with Satan and those other fallen angels. They are those who deny the Holy Spirit, which is not something the average man can do. Very few have been identified as committing the unpardonable sin. One we know of is Cain, who slew Able, another is possibly Judas Iscariot. Both men knew God, walked in his presence, and denied him to his face.


How did the Roman Punishment "cross" became a holy symbol to Christians?

In mosaic law the Priests would offer sacrifice and do this on a table, the table was referred to as an alter.  Christ who offered himself up as a sacrifice for all, offered himself up on a Cross. His symbol is often referred to as a tree.

In the Catholic Church when you enter into the sanctuary you bow down to three places mostly. First to the tabernacle (if the candle is lit, at the last few days of lent the Lord is removed from the tabernacle). You bow there with adoration as if (because he is there) you are bowing before Christ himself.  Then to the alter of sacrifice which is a veneration rather than an adoration,  and then to the cross itself as if to aide in your mind the fact that where you stand is Calvery at the foot of the Cross with Mary the Mother of the Lord, where Christ continually offers himself to God The Father daily. Not a new sacrifice but he same sacrifice re-presented.

Being Holy means being set apart. A cross used by Roman executioners means nothing, but a cross with the Lord hanging from it now that is Christ Crucified and that is what the Church Preaches.  Anything else is simply two sticks or a cross empty of Christ.


Do Seventh Day Adventists believe people who attend church on Sunday will go to hell?

Do Seventh Day adventists believe that people who go to church on Sunday will go to hell?

No we do not, we believe only those who are unfaithful to God will be not be in heaven.

The Bible is clear that God has His people in many denominations. In Revelation 18:4, a voice is heard in heaven saying:

  "Come out of her, my people, lest you share in her sins, and lest you receive of her plagues." (Revelation 18:4)

There is also a common misconception that we believe Sunday keeping is the mark of the beast. But it is not. Only when Sunday keeping is a forced day of worship, restricting freedom of conscience, do we consider it the mark of the beast. The writings of Ellen White in SDA Bible commentary explains:

  "Sundaykeeping is not yet the mark of the beast, and will not be until the decree goes forth causing men to worship this idol sabbath. The time will come when this day will be the test, but that time has not come yet." The S.D.A. Bible Commentary 7:977 (1899).

However, this is not to say that the Sabbath is not a test today, because it is. True observance of the fourth commandment is an outward sign of loyalty to God, just like the rest of the ten. Only that we are not able to say who has received this light and who has not.

  "We shall not be held accountable for the light that has not reached our perception, but for that which we have resisted and refused. A man could not apprehend the truth which had never been presented to him, and therefore could not be condemned for light he had never had."—The S.D.A. Bible Commentary 5:1145 (1893).

The truth is Adventists within the same denomination will differ in their conviction of how much/ to how many God has revealed this light to today. Many have grandparents or relatives in Sunday churches, so it is a sensitive issue. More liberal Adventists believe that unless you are 100% convinced, you are perfectly fine to attend Sunday keeping churches. However, more conservative Adventists believe that many Sunday goers have heard of the Sabbath, but have neglected to study further and have quietened their conscience to a degree in breaking this commandment in favour of tradition, and thus will be held accountable.

Either way, what we do agree on is that no one is really saved by keeping Sunday or Sabbath, but by our faithfulness to Jesus and willingness to follow the lamb wherever He goes (Revelation 14:4). We will see many Sunday goers in heaven, especially those who lived in the middle ages when the Sabbath truth was lost to many.


In what manner does the LDS believe we may become like God?

The issue here is that your trying to find something that's not there.

The doctrine is simple and plainly stated by the prophet just as you quoted:

  As man is, God once was; as God is, man may become.

That's it, there is nothing else to it.

If you want a scriptural reference from the New Testament:

  Romans 8:16-17, 16) The spirit itself beareth witness with our spirit, that we are the children of God: 17) And if children, then heirs; heirs of God, and joint-heirs with Christ; if so be that we suffer with him that we may be also glorified together. [bold mine]

That is the basis of the entire belief for Latter-Day-Saints. We are children of our Heavenly Father and eventually we may become like Him, in ALL His glory.


How can we reconcile Judges 10:13 with Numbers 23:19?

There seems to be a difference between a change of mind, and being interactive, and a change of mood.
Earlier God gave them the choice:

Deuterenomy 30:15-18 (NIV)

  15 See, I set before you today life and prosperity, death and destruction. 16 For I command you today to love the Lord your God, to walk in obedience to him, and to keep his commands, decrees and laws; then you will live and increase, and the Lord your God will bless you in the land you are entering to possess. 17 But if your heart turns away and you are not obedient, and if you are drawn away to bow down to other gods and worship them, 18 I declare to you this day that you will certainly be destroyed. You will not live long in the land you are crossing the Jordan to enter and possess.

The situation in Judges refers to the fact that the nation did not continue to follow him, so they had to face the consequences as stated before. They were about to be destroyed, and God did not intend to help them, if they would not worship him and worship other gods (as in the agreement in Deuteronomy). And God informed them about it In Judges 10:13, as you quoted.

In response to his warning for the coming destruction, they responded (Judges 10:15):

  15 But the Israelites said to the Lord, “We have sinned. Do with us
  whatever you think best, but please rescue us now.” 16 Then they got
  rid of the foreign gods among them and served the Lord. And he could
  bear Israel’s misery no longer.

So because they repented and changed their behaviour, God reacted according to their reaction and saved them.

Since the messages and actions of God in these examples are all according the earlier stated principles, it would be harsh to say that God was self contradictory or changed his mind. He just reacted according to their behaviour, and how they used their free will.

To me the example closest to change of mind in the bible is in Genesis 6:5-8 (NIV)

  5 The Lord saw how great the wickedness of the human race had become
  on the earth, and that every inclination of the thoughts of the human
  heart was only evil all the time. 6 The Lord regretted that he had
  made human beings on the earth, and his heart was deeply troubled. 7 So
  the Lord said, “I will wipe from the face of the earth the human race
  I have created—and with them the animals, the birds and the creatures
  that move along the ground—for I regret that I have made them.” 8 But
  Noah found favor in the eyes of the Lord.

It seems that Gods state is adaptive to human behaviour and free will. Assuming divine inspiration, it is interesting that Gods promises to stand by his principles, but also wants to express the "feelings" (that it is difficult to do so), when people are abandoning his standards all the time.


If justification is an event, when does it happen?

According to most independent, fundamentalist Baptists, (and to the best of my knowledge, the groups that you mentioned) justification is a one-time event that happens at the moment of conversion, when a sinner repents on his or her sins and puts their faith in Christ for salvation.

This would be in line with a Calvinist view.  Justification is a result of salvation, and is something granted freely as the gift of salvation, apart from any works of man.

The very same Wikipedia article that you linked to outlines the relationship between Justification and Sola Fide, for those denominations that subscribe to the view that salvation is by faith alone.

This article covers more groups independently, rather than lumping protestants entirely into a group, and may provide more clarity on how different denominations view the topic.


It Still Confuses Me: Who can receive Communion where (Catholic/Orthodox)?

The Catholic Church permits the Orthodox to receive the Eucharist in a Catholic service, but cautions them to observe their own disciplines. For example, OSCCB offers:

  Members of the Orthodox Churches, the Assyrian Church of the East, and the Polish National Catholic Church are urged to respect the discipline of their own Churches. According to Roman Catholic discipline, the Code of Canon Law does not object to the reception of Communion by Christians of these Churches (canon 844 §3).

The Catholic Church permits a Catholic to receive in an Orthodox service if a Catholic service is not available:

  Whenever necessity requires it or true spiritual advantage suggests it, and provided that danger of error or of indifferentism is avoided, the Christian faithful for whom it is physically or morally impossible to approach a Catholic minister are permitted to receive the sacraments of penance, Eucharist, and anointing of the sick from non-Catholic ministers in whose Churches these sacraments are valid.(canon 844 §2)

The appropriate sections of the canon law can be found here.

According to the Orthodox Church, the Orthodox may not receive the Eucharist in a Roman Catholic Church. For example, the OCA offers this answer:

  Further, Orthodox Christianity does not permit its faithful to receive Holy Communion in non-Orthodox communities, whether they be Roman Catholic, Protestant, or whatever. Hence, while Roman Catholicism may extend Eucharistic hospitality to Orthodox Christians, it does not mean that Orthodox Christians are permitted to accept such hospitality.

Further, non-Orthodox can not receive in an Orthodox service:

  Because a non-Orthodox individual has chosen not to embrace all that Orthodox Christianity holds, the non-Orthodox individual makes it impossible for an Orthodox priest to offer him or her communion.

Before the Great Schism, there was no formal separation between East and West.


According to Scripture, is sacrifice a requirement for salvation?

What is salvation according to Scripture?

The OP has the right understanding. People are saved from their sins by Jesus

  Matt 1:21 (RSVCE) 21 she will bear a son, and you shall call
  his name Jesus, for he will save his people from their sins.”

Why is a sacrifice required?

Again OP has a right understanding. God is good, merciful and just. In justice, atonement for sin needs to be made, in his mercy, he has provided for forgiveness of sin. He has required sacrifice to achieve both ends. Saint Paul explains in Roman 5:1-10

  5 For every high priest chosen from among men is appointed to act on behalf of men in relation to God, to offer gifts and sacrifices for
  sins. 2 He can deal gently with the ignorant and wayward, since he
  himself is beset with weakness. 3 Because of this he is bound to offer
  sacrifice for his own sins as well as for those of the people. 4 And
  one does not take the honor upon himself, but he is called by God,
  just as Aaron was.

  5 So also Christ did not exalt himself to be made a high priest, but
  was appointed by him who said to him,

  “Thou art my Son, today I have begotten thee”;[a] 6 as he
  says also in another place,

  “Thou art a priest for ever, after the order of Melchiz′edek.” 7 In
  the days of his flesh, Jesus[b] offered up prayers and
  supplications, with loud cries and tears, to him who was able to save
  him from death, and he was heard for his godly fear. 8 Although he was
  a Son, he learned obedience through what he suffered; 9 and being made
  perfect he became the source of eternal salvation to all who obey him,
  10 being designated by God a high priest after the order of
  Melchiz′edek.

  a. If Jesus was to be mediator, he had to have a human nature
  like ours, and, moreover, he could not appoint himself, but had to be
  appointed by God.
  b. Greek he

What is sacrifice?

  SACRIFICE The highest form of adoration, in which a duly authorized
  priest in the name of the people offers a victim in acknowledgment of
  God's supreme dominion and of total human dependence on God. The
  victim is at least partially removed from human use and to that extent
  more or less destroyed as an act of submission to the divine majesty.
  Thus a sacrifice is not only an oblation. Where an oblation offers
  something to God, a sacrifice immolates or gives up what is offered.
  In sacrifice the gift offered is something precious completely
  surrendered by the one making the sacrifice as a token of humble
  recognition of God's sovereignty. (Etym. Latin sacrum, holy, sacred
  + facere, to make, do.) - Dictionary: SACRIFICE | Catholic Culture

All the acceptable sacrifices in the Old testament were a type of Jesus' sacrifice. Jesus' sacrifice is the one that actually effects forgiveness of sins past, present and future.

  Matt (RSVCE) 28 for this is my blood of the [new] covenant,
  which is poured out for many for the forgiveness of sins.


Where do Christians believe the Qur'an came from?

The "prophet" Muhammad stated that the angel Gabriel visited him with revelation and he put great importance upon Gabriel.

This is not true.  Not if you are talking about the Koran, which never says this.  This information comes from the Hadiths.  If you were to base your understanding of Mohammed purely on his writings (i.e. the Koran) and not on the hearsay stories of later Muslim tradition, you would not come to the conclusion that Mohammed said anything about Gabriel.

The way Mohammed presents it in the Koran, it sounds like he's claiming Allah himself is speaking to him. There is no specific mention of Gabriel doing anything with revelation, other than in Sura 2:97-98 which is easy to miss. In fact, Michael is mentioned in the same context. Nowhere in the Koran does Mohammed specifically claim that any of his "revelation" comes from Gabriel. This specific place seems to be making Gabriel "confirm" the message (similarly to the Holy Spirit in Christianity) and that anyone who rejects revelation is an enemy of Gabriel and Michael and all the angels.

In point of fact, Sura 2:98 doesn't even specifically call Gabriel and Michael angels, but may even intend them to be human messengers, for it says "Whoever is the enemy of Allah and His angels and His messengers and Jibreel and Meekaeel, so surely Allah is the enemy of the unbelievers."  It could even be taken that Gabriel and Michael are being placed in a third category all their own, and not among the angels nor the messengers.  This would not be surprising considering the very low state of Mohammed's biblical knowledge (to be discussed below).

A reading of Mohammed's book (i.e. the Koran) will show that he pieced his "revelation" together from Bible stories that he heard taught (he obviously didn't read the Bible) and from stories and legends taken from the Talmud which he heard (e.g. the angels being commanded to worship Adam) and from Pagan stories which he heard (e.g. "God's own she-camel").

That he did not receive his information from any angel nor from actually reading the Bible is clear from how he mangles Bible stories, like getting Haman from the book of Esther into the story of Moses, and making Haman the builder of the tower of Babel, in Moses' day, by having Pharaoh say to Haman "Build me a tower so I can climb to heaven and see Moses' God." (Koran, in Sura 28:38 and Sura 40:36-37)

The Koran also confuses Mary the mother of Jesus with Miriam the sister of Moses, explicitly calling Mary "the daughter of Amram" (or Imram) and "sister of Aaron" several times.  Its pretty clear that Mohammed has no sense of chronology, and thinks that Jesus was Moses' nephew and received the Injeel (Gospel) not long after Moses received the Tavrat (Torah), perhaps only a decade or so later.

This kind of mixing up of various biblical stories into one can only occur as a result of being illiterate, of not having read the Bible, and of accidentally mixing up stories you heard in your head. It would be hard to completely lack a sense of chronology if you had actually read the Bible.  Surely nobody would mix up stories this badly on purpose. And surely no angel would be malevolent enough to play a dirty trick like this on anyone, or at least Gabriel would not.

Edit: In response to comments citing particular verses of the Koran which supposedly give Gabriel a more prominent place than I've suggested above.  We must remember that the Koran is not like the Bible.  You can't just translate the Koran with a formal-equivalence type translational methodology, because it will come out as ungrammatical jibberish.  Muslims admit as much by teaching that "the Koran in untranslatable" and therefore they claim that to really read the Koran you must read it in Arabic.  Contrary to this, the KJV translators write in their preface that even the "meanest" (i.e. roughest) translation of the Bible is still the word of God.  The reason is we don't have to supplement a bunch of tradition and stuff from other sources to even end up with a grammatical sentence when translating the Bible. But with the Koran, you pretty much do.  So without Islamic tradition and all the details that it adds about Gabriel and so on, it would be very hard to produce a translation of the Koran that's even barely readable. If you were, however, to attempt to wade through a literal, formal-equivalence, translation of the Koran, you would find all this stuff about Gabriel and several other things to be missing.  This is another proof, in my estimation, that the Koran does not come from any kind of supernatural source, neither from God or any angel, nor from Satan or any demon, but merely from the mind of a man.


Why did Adam claim he was "naked" before God when he and Eve had clothed themselves with fig leaves?

The Nakedness was not merely physical in nature

It's important to note that this is Adam's claim--not God's.  Adam and Eve had indeed taken measures to clothe their nakedness after their sin.  Before sin, when they were both in a state of innocence, it seems they felt no need for clothing.  This is akin to a young child who experiences no shame in being unclothed, much to the chagrin of his parents.

Adam and Eve's clothing appears to have been sufficient in relation to one another.  However, as soon as God enters the picture, the insufficiency of their own efforts becomes apparent.

It seems, then, that mankind's efforts to cover over their own sin may be sufficient among others who have sinned, but it is insufficient in the presence of God.

If Adam's nakedness had merely been physical, then physical clothing would have been sufficient to cover over his shame.  The shame, however, was not merely physical and neither was his sin.  It was also a spiritual act of defiance toward God.

God's Provision

It's interesting to note that later in the chapter, God makes clothing for Adam and Eve.  We must wonder what the fig leaves were insufficient and why God considered other clothing to be superior.

The nature of the clothing provided by God is that they were from the skins of an animal.  Although this is not explicitly stated, it seems reasonable to conclude that this was the first substitutionary sacrifice.  An animal had to die to provide the animal skins for that clothing.  The death of the innocent animal was sufficient to cover the shame of sin, yet it was insufficient to atone for the guilt, since Adam and Eve were still banished from the garden.

While the sacrifice of the innocent covered over the shame of sin, it would require the sacrifice of the Righteous One (Jesus) to atone for the guilt.

The physical clothing made by God is then a picture of the spiritual clothing that would be provided through the atoning sacrifice of Jesus Christ.

The New Testament speaks of a type of clothing that comes to followers of Christ:

  You are all sons of God through faith in Christ Jesus, for all of
  you who were baptized into Christ have clothed yourselves with Christ. Galatians 3:26-27

  Now we know that if the earthly tent we live in is destroyed, we have
  a building from God, an eternal house in heaven, not built by human
  hands. Meanwhile we groan, longing to be clothed with our heavenly
  dwelling, because when we are clothed, we will not be found naked. For
  while we are in this tent, we groan and are burdened, because we do
  not wish to be unclothed but to be clothed with our heavenly dwelling,
  so that what is mortal may be swallowed up by life.  2 Corinthians
  5:1-2

So, Adam was not naked at that time in a physical sense, but he was still naked (exposed, in a state of shame) in a spiritual sense.


Why did Zechariah's neighbours make signs to him?

It was an unusual practice at the time to name a son after his father, because a man tended to be identified as, for example, (John) son of (Zechariah), i.e., (John), Bar-(Zechariah); and Zechariah Bar-Zechariah would have been strange.

Matthew Henry claims that Zechariah was both deaf and mute (cf. 1:22, 64), so they appealed to him by means of signs. He responded by means of writing (1:63). These two infirmities are often associated with each other (cf. Mark 7:32, 37; 9:25). But here I find the point strained.

Since the naming of the child typically fell to the father, the "crowd" would naturally be gesturing to Zechariah for his validation of Elizabeth's "announcement." Thus, in Luke 1:63 he asked for a writing tablet, which consisted of a wood tablet (a pinakidion) covered with wax.

To everyone’s amazement he wrote, “His name is John.” So why the amazement? Most likely because “John” was not a name used in their family. The proponents of Zechariah's deafness obviously believe that Zechariah was not able to hear Elizabeth’s choice of this name, but, again, this is strained exegesis. Since Zechariah was mute, he could not “say” anything. His only means of confirming the name of the boy was John was to write it down for the onlookers.


Why did the reformers include the book of Hebrews in the canon?

As far as Calvin was concerned, his views on the canonicity of Hebrews can be found in his introductory comments to his commentary on Hebrews (here at pp. 16–17). He includes it "without hesitation" as part of the New Testament Canon. The factors in reaching that conclusion were:

Its acceptance by the early church. This is why he feels the need to
point out (and then explain away) that the Latin churches were slow
to accept it. Calvin states that they were concerned Hebrews might
support the Novatian heresy (the refusal to allow forgiveness to
those who had once abandoned the faith in the persecution of the
emperor Decius). He then undertakes to explain in the commentary why
such fears were groundless.

  Not only various opinions were formerly entertained as to the author of this Epistle, but it was only at a late period that it was received by the Latin Churches. They suspected that it favored Novatus in denying pardon to the fallen; but that this was a groundless opinion will be shown by various passages.

Its content, which has value and is consistent with the themes of
the rest of the gospel.

  There is, indeed, no book in the Holy Scriptures which speaks so clearly of the priesthood of Christ, so highly exalts the virtue and dignity of that only true sacrifice which he offered by his death, so abundantly treats of the use of ceremonies as well as of their abrogation, and, in a word, so fully explains that Christ is the end of the Law. Let us not therefore suffer the Church of God nor ourselves to be deprived of so great a benefit, but firmly defend the possession of it.

Its authorship. For Calvin this is a secondary basis. ("We need not
be very solicitous.") Calvin discusses the historical views on this
but himself rejects Paul on grounds of both content and style.

The full text of Calvin's opening comments reads as follows:

  Not only various opinions were formerly entertained as to the author of this Epistle, but it was only at a late period that it was received by the Latin Churches. They suspected that it favored Novatus in denying pardon to the fallen; but that this was a groundless opinion will be shown by various passages. I, indeed, without hesitation, class it among apostolical writings; nor do I doubt but that it has been through the craft of Satan that any have been led to dispute its authority. There is, indeed, no book in the Holy Scriptures which speaks so clearly of the priesthood of Christ, so highly exalts the virtue and dignity of that only true sacrifice which he offered by his death, so abundantly treats of the use of ceremonies as well as of their abrogation, and, in a word, so fully explains that Christ is the end of the Law. Let us not therefore suffer the Church of God nor ourselves to be deprived of so great a benefit, but firmly defend the possession of it.

  Moreover, as to its author, we need not be very solicitous. Some think the author to have been Paul, others Luke, others Barnabas, and others Clement, as Jerome relates; yet Eusebius, in his sixth book of his Church History, mentions only Luke and Clement. I well know that in the time of Chrysostom it was everywhere classed by the Greeks among the Pauline Epistles; but the Latins thought otherwise, even those who were nearest to the times of the Apostles.

  I indeed, can adduce no reason to show that Paul was its author; for they who say that he designedly suppressed his name because it was hateful to the Jews, bring nothing to the purpose; for why, then, did he mention the name of Timothy as by this he betrayed himself. But the manner it of teaching, and the style, sufficiently show that Paul was not the author; and the writer himself confesses in the second chapter that he was one of the disciples of the Apostles, which is wholly different from the way in which Paul spoke of himself. Besides, what is said of the practice of catechizing in the sixth chapter, does not well suit the time or age of Paul. There are other things which we shall notice in their proper places.

  What excuse is usually made as to the style I well know that is, that no opinion can be hence formed, because the Greek is a translation made from the Hebrew by Luke or someone else. But this conjecture can be easily refuted: to pass by other places quoted from Scripture, on the supposition that the Epistle was written in Hebrew, there would have been no allusion to the word Testament, on which the writer so much dwells; what he says of a Testament, in the ninth chapter, could not have been drawn from any other fountain than from the Greek word; for διαθήκη has two meanings in Greek, while |berit| in Hebrew means only a covenant. This reason alone is enough to convince men of sound judgment that the epistle was written in the Greek languages. Now, what is objected on the other hand, that it is more probable that the Apostle wrote to the Jews in their own language, has no weight in it; for how few then understood their ancient language? Each had learned the language of the country where he dwelt. Besides, the Greek was then more widely known than all other languages.


How novel is John Paul II's theology of the family as "ecclesia domestica"?

Please consider this only the start of an answer, I don't know too much about it and the Internet isn't much help.

My wife and I participated in a Marriage Encounter Weekend, part of Worldwide Marriage Encounter (WWME) this weekend and it was mentioned the idea of "Little Churches". In the back of the booklet there was a timeline that gave the progression of events that led to the creation of the WWME community.

It's very beginning is traced back to the conferences given by Spanish Priest, Fr. Gabriel Calvo starting in 1952 as part of the "Marriage teams of Pope Pius XII".

There was a teaching, which for your benefit although it made me sound like a know-it-all doorknob Catholic. I specifically asked one of the facilitators about one of the ideas in the weekend called "Little Churches", where it is specifically mentioned, although not attributed to any pope or council, the idea that the family is a little church.  I asked him if it came from John Paul II, and he said yeah, the Theology of the Body has a lot to do with the ideas WWME incorporates into the presentations (although certainly not explicitly), but the Little Church idea was present in his first encounter, which was 30 years ago.

So, that doesn't particularly help since the time-line puts it at the same time.  But I'd be hard-pressed to assume that particular theological point (as pertinent was it is) would get incorporated into WWME that quickly, which was clearly a product of the 1960's.  I almost think the Pope was more influenced by them than the other way around!


How to appropriately reply to "You're going to hell"?

How to reply to “You're going to hell”?

”May God mercy on my soul and yours as well.” And remember well that we will both face our Eternal Judge some day!

  "May God have mercy upon your soul" or "may God have mercy on your soul" is a phrase used within courts in various legal systems by judges pronouncing a sentence of death upon a person found guilty of a crime that requires a death sentence. The phrase originated in beth din courts in the Kingdom of Israel as a way to attribute God as the highest authority in law. The usage of the phrase later spread to England and Wales' legal system and from there to usage throughout the colonies of the British Empire whenever a death sentence was passed.

  Depending on where it is used, the phrase has had different emphasis through the years. It was formally intended as a prayer for the soul of the condemned. However, in later times, particularly in the United States, it has only been said as a result of legal tradition where the religious meaning and origin is not founded on belief. - May God have mercy upon your soul


According to the Church of England, if humans have free will, why do we ask for things in prayer?

I don't think there's any official C of E doctrine about this.

I think it's worth remembering that prayer is not any kind of magic spell, and that the Almighty is not bound by space and time. Conversing with the Lord about what you'd like to happen is one thing; being disgruntled when you don't get what you asked for, as if the Lord were a genie from a lamp, is another. And your question makes a distinction between the natural laws of the universe and the action of God, as if they were separate things. They aren't, any more than God's work of sanctification in you is a separate thing from you trying to do good works.


How do Orthodox Christians explain that the Father and the Son are not two different Gods?

The two Creeds are not different in respect of there being two/three Gods, because there is only one God, period. What's different is the "emphasis" of the two Creeds. The following explains it.
"The chief difference between the Nicene Creed and the Athanasian Creed is one of emphasis. The Nicene Creed emphasized the full deity of the Son and of the Holy Ghost and it only implies, rather than explicitly explains the oneness of God. The Athanasian Creed, leaving nothing to be assumed, brings in the idea of the inviolate Oneness of God (there is only one God, not three.) 8. The Athanasian Creed also deals with one additional error. At the time there were controversies being raised by some about the person and nature of Jesus Christ and whether or not He was both true God and true man. All of the rationalizations, in one way or another, either removed from Jesus his true humanity or his true divinity or the idea that there was just one Jesus who was both true God and true man. 9. The Church Year: Early Christians took the incarnation very seriously: They expected to follow the life example of Christ. They followed the church calendar through the various segments of Christ’s life. In the Western Churches, the Church Year was and remains to this day, divided into two almost-equal parts: the first some have called “The Life of Christ” while the second is “The Christian Life.” 10. The Year begins with Advent – a time of reflection in anticipation of the coming of Christ. Advent is followed by Epiphany, celebrating the revealing of Christ as God’s anointed one." https://www.coursehero.com/file/p5g865/The-chief-difference-between-the-Nicene-Creed-and-the-Athanasian-Creed-is-one/
You might find the following article informative as it relates to the "Patristic" fathers. https://www.monergism.com/thethreshold/articles/onsite/qna/patristics.html


Where does the Bible stand on vegetarianism?

Romans 14  as a whole doesn't endorse a vegetarian diet as necessary or otherwise better. Look at the beginning of the chapter for the context:

  Romans 14:1-4 (KJV)

  1 Him that is weak in the faith receive ye, but not to doubtful
  disputations.

  2 For one believeth that he may eat all things: another, who is weak,
  eateth herbs.

  3 Let not him that eateth despise him that eateth not; and let not him
  which eateth not judge him that eateth: for God hath received him.

  4 Who art thou that judgest another man's servant? to his own master
  he standeth or falleth. Yea, he shall be holden up: for God is able to
  make him stand.

What Paul is saying is that some believe it is better not to eat meat, and that if he is in such a case as to be a cause of temptation for such a brother, he would rather not eat meat at all so that his brother is not tempted. This is the same problem as wine in a way, in that wine is not bad in itself, but it is better to not drink wine if it will cause a brother or sister to stumble.

Paul is not saying that it is better to be a vegetarian, but he is warning to not let such fleshy matters be reasons for brothers or sisters to stumble. In other words, I'd say if you are eating with someone who believes being a vegetarian is better, don't argue on it, just go with it so it doesn't become a subject of stumble for this brother or sister.


How do Catholics and Eastern Orthodox justify their clergy praying with those big hats on their heads?

Orthodox bishops, priests and monks always remove their hats (of whatever kind) when praying.  The Bishop removes his mitre at the Altar.  Monks hang their klobuk over their shoulder or remove it entirely during the service.  So the question seems to stem from ignorance, or not actually attending an Orthodox Liturgy to see what we do.  Incidentally it is correct for monks (and Orthodox bishops are monks) to keep their klobuks on during much of the Offices.


Have Jehovah's Witnesses always been politically neutral?

Have JWs always been politically neutral, or did they in the past e.g. vote in elections or support one party over another?

The majority of history I can find about Jehovah's Witnesses having political neutrality is regarding being conscripted for war. Specific dates are hard to come by, but war neutrality was first widely encouraged in 1904, followed by another refinement in the Sep. 1, 1915 Watchtower, and then finally adopted completely with the landmark article titled "Neutrality" in the Nov. 1, 1939 Watchtower. (Source)

The Bible Students, now known as Jehovah's Witnesses, knew from early on of John 18:36, which discusses how God's Kingdom is not part of this world. I can only speculate, but the consciences of those early Bible Students probably kept them from needlessly involving themselves in politics. Most controversial standpoints at that time were about how to react to compulsive military service.

  Does this political neutrality thing mean that JWs do not meet with U.S. Presidents or other political leaders to discuss policies, or have such meetings ever happened?

Jehovah's Witnesses don't discuss politics with anyone. They're completely neutral for the sake of giving exclusive devotion to God's Kingdom. This is advantageous both for the purposes of ministering to "people of all the nations" (Matthew 28:19) and for the purposes of having unity within the congregation (Psalm 133:1).

JWs do assign much respect to local authorities, and would not refuse meeting with the authorities, but they would not give opinions on politics or promote a political campaign.

  Does it mean that JWs do not sing national anthems such as "Star Spangled Banner" as part of their church services?

Correct. At football games, baseball games, etc. I usually excuse myself during the beginning of the game and go walk around in order to avoid making a scene, but during these ceremonies some JWs will remain seated, others will perhaps stand up but not put their hand on their heart. This isn't meant to be seen as defiance, only as non-participation.

Likewise, in all 13 years I went to public school in the United States, I would just stand respectfully during the Pledge of Allegiance. People very rarely asked me why.


In what order were the 12 Apostles called?

The word “disciple” refers to a learner or follower. The word “apostle” means “one who is sent out.” While Jesus was on earth, his twelve followers were called disciples.  After his resurrection and ascension, Jesus sent the disciples out to be His witnesses (Matthew 28:18-20; Acts 1:8). They were then referred to as the twelve apostles. However, even when Jesus was still on earth, the terms “disciples” and “apostles” were used somewhat interchangeably.

The original twelve disciples/apostles are listed in Matthew 10:2–4: “These are the names of the twelve apostles: first, Simon (who is called Peter) and his brother Andrew; James son of Zebedee, and his brother John; Philip and Bartholomew; Thomas and Matthew the tax collector; James son of Alphaeus, and Thaddaeus; Simon the Zealot and Judas Iscariot, who betrayed Him.”

The Bible also lists the twelve disciples/apostles in Mark 3:16–19: “He appointed the twelve: Simon (to whom he gave the name Peter); James the son of Zebedee and John the brother of James (to whom he gave the name Boanerges, that is, Sons of Thunder); Andrew, and Philip, and Bartholomew, and Matthew, and Thomas, and James the son of Alphaeus, and Thaddaeus, and Simon the Zealot, and Judas Iscariot, who betrayed him.”

Here is the list of the original twelve in Luke 6:13–16: “And when day came, he called his disciples and chose from them twelve, whom he named apostles: Simon, whom he named Peter, and Andrew his brother, and James and John, and Philip, and Bartholomew, and Matthew, and Thomas, and James the son of Alphaeus, and Simon who was called the Zealot, and Judas the son of James, and Judas Iscariot, who became a traitor.”

A comparison of the three passages shows a couple of minor differences in the names. It seems that Thaddaeus was also known as “Judas, son of James” (Luke 6:16). Simon the Zealot was also known as Simon the Canaanite (Mark 3:18). The Gospel of John uses the name “Nathanael” instead of “Bartholomew,” but Nathanael and Bartholomew were undoubtedly the same person. Judas Iscariot, who betrayed Jesus, was replaced in the twelve apostles by Matthias (see Acts 1:20–26).

Luke 6:12-13 shows the 12 were all called by Jesus on the same day.  Jesus spent the night in prayer prior to selecting his 12 apostles from his disciples.

Edit: John 1:35-50 sheds some light on the order in which Jesus first met his disciples. Andrew (son of John) first met Jesus then called his brother Simon (Peter) and said "we have found the Messiah." Then Philip (also a fisherman from Bethsaida) meets Jesus and tells Nathaniel (or Bartholomew).

Matthew, Mark and Luke mention James and John (sons of Zebedee) and Mark and Luke mention Levi, son of Alphaeus, the tax collector (Matthew)

That leaves Thomas, James (son of Alphaeus), Thaddaeus (or Judas the son of James) and Simon the Zealot (Simon the Canaanite) unaccounted for.  Judas, son of Simon Iscariot, is mentioned in John 6:71.


Why was having concubines not a sin like adultery?

Having multiple wives was permitted (though not exactly endorsed) in the Law of Moses.

Adultery is having (or desiring) an intimate relationship with someone who's already married (to someone else). As it was forbidden in the Mosaic law, it was referring to a man and someone else's wife. It was not really speaking of a married man and another woman. Even then, though, the only occasion in which such a relationship is allowed is within marriage. So, in order for a man to have that kind of relationship with a woman, she would have to be a wife of some kind.

Concubines were essentially wives of lower status. They were still bound to the one man.


Why are the Jesuits and Society of the Sacred Heart gender specific?

The Society of Jesus and the Society of the Sacred Heart are both religious orders. All Catholic religious orders are by definition either for men or for women.

As to why this is... Well, historical Catholic understanding gave very different roles to men and women both in normal life and in the sphere of religion. Men, for instance, had priestly roles, preaching roles, roles teaching in universities and the like. Women, by contrast, had roles that mainly consisted of charitable works and, in recent centuries, the education of girls. They were distinctly different roles, and therefore had entirely different orders.


In the Eastern Orthodox tradition, is it possible to laicize a bishop?

It appears that for autocephalous Orthodox Churches, their Holy Synod has the authority to laicize them.
Although the person in question was "demoted" to monk and not fully laicized, I believe I have found an illustrative and extremely recent example (Wikipedia, which I quote below [editing out the references]; news source). The person in question, Monk Seraphim (Storheim), was convicted of sexually assaulting a young boy.

Following his release from prison, members of the Holy Synod of Bishops of the Orthodox Church in America on October 19–23, 2015 canonically deposed the retired Archbishop Seraphim from the status and all sacred functions of the episcopacy, removed him from the ranks of the clergy, and returned him to the status of a lay monk.

The Holy Synod made this decision with much sorrow, but with the conviction that it was a necessary action both for the salvation of the now Monk Seraphim and for the preservation of the good order and stability of the flock of Christ. At the same time, we offer our prayers for the victims, their families and all those who have been affected by the events surrounding this case.

Edited to add: With respect to your second question, I found this article on Professor Contantine Scouteris at the University of Athens on Christian Priesthood and Ecclesial Unity: Some Theological and Canonical Considerations. I have edited out the references again, but the original website has them. It appears that there is some debate on the matter, but at least some thinkers (such as Scouteris, with canonical basis) reject the idea of an indelible mark.

[...]the priest does not possess in himself an indelible mark as if it were a magical seal which grant him a private efficacy to perform the Eucharist or any other liturgical action, apart from the ecclesial body. The priestly ministry is rather a charismatic gift to serve and edify the body of the Church. It is a permanent rank of service only in union and by the discerning authority of the Church.

The doctrine of the "indelible mark" attained at ordination to the priesthood seems to have originated in the Scholastic period of the Western Church. This same conception was at times borrowed by Eastern theologians thereafter. [...] It is interesting to mention here that the sixth Ecumenical Council in its 33rd canon condemns the practice of Armenian Christians who had embraced the Old Testament custom concerning the Levitic rank and did not accept for the priesthood anyone who was not of this so called "priestly lineage". The reasoning for the adoption of the Old Testament typology in both cases seems to be that an identification mark is a constitutive element of priesthood. In the later case it is conceived as an inherited trait, while in the former which concerns us here, it is viewed as irrevocably and individually attained at the ordination rite.

The logical conclusion of the "indelible mark" is that the ordained individual possesses forever this peculiar mark of priesthood which can never be removed by anyone nor can it be surrendered in any circumstance. [...] Thus the ordained person possess a self sufficient power which is higher than the Church itself And the Church is not able to take back the indelible mark from an individual even if he is defrocked and excommunicated.

Interpreting the 68th Apostolic Cannon which refers to the impossibility of repeating the sacrament of ordination, St. Nicodimos the Agiorite explains that ordination cannot be repeated because it is done according to the Type of the First and Great Priest who entered once and for all into the holy of holies and there granted eternal salvation. Yet, he unswervingly rejects the doctrine of the "indelible mark" of priesthood and attests that it is the "invention of scholastics." Nevertheless, according to St. Nicodimos, the doctrine is borrowed by Nicholas Bulgaris, Koresios and many other theologians of the past century and some still somehow adhere to it today.


Are modern Amish much more dissimilar from society than the original generations of Amish?

Perhaps at the outset it should be noted that the Amish descended from one of the two main leaders within the Swiss Brethren Anabaptists (soon after called Mennonites) in the 1690s, named Jakob Ammann, who, along with his supporters, eventually split from that body. Most accounts have portrayed Ammann as an abrupt and unyielding leader who demanded a demonstrably pure lifestyle by church members to the point of insisting on applying the "ban" to them when they failed in that regard. This was also known as "social shunning" (based on a scriptural passage) and was viewed as too judgmental by the opposing group within the fellowship.

Consequently, the Amish group withdrew, even being called Amish-Mennonites since they still adhered to the general Mennonite doctrines and continued on their own course even after Ammann died, most of whom emigrated to Pennsylvania, USA, initially in the early 1700s, while yet others from the Alsace-Lorraine area in the mid-1800s emigrated to Southwestern Ontario, Canada, this latter group being my own ancestors. But as it was mentioned in the question above, to this point in time, the Amish would not have stood out nearly as much from the culture surrounding them as they do now because technology wasn't so much the vehicle of their expression of being faithful to their doctrines and to the mindset of their former leader. Surely, their social isolation would have been noted, but as my father told me, it wasn't until the turn of the 20th-century when the automobile and electricity emerged that they then began to make a conscious decision to reject those as being a corrupting influence leading them into unfaithfulness and "worldliness," as my late mother would refer to when informing me about how it was explained to her.

Now, I must say that my direct ancestors did not stay with the Amish who withdrew to an even greater extent in the early 1900s but instead joined with the larger Mennonite body who did not associate technological progress directly with unfaithfulness. And so, it appears that it was during that first decade of the 1900s when the Amish really became earnest about ostensibly "freezing" their lifestyle.


Can theology still be defined "the science of faith"?

Yes, the term is applicable to theology. Let's break it down to see why.

The first word is science. At its root, the word simply means knowledge. Many people forget that and the word has been somewhat hijacked to mean exclusively study about the natural world derived from facts and experiments, or more properly, the scientific method. The scientific method is a science in its own, but it is not science in whole.

The second word is faith. First, the word simply means having complete trust in something. You can have faith in just about anything, and hopefully you would have a reason to do so. I can have faith in a person to do the right thing, which might be based on our shared experiences. I can have faith in the scientific method to provide the best current understanding about something, which might be based on the history of its use. And, of course, I can have faith in God, that he is there and cares about us, that he will keep his word, that Christ will return, and that eternal life awaits for those who love Him. This can be based on any number of things including, apologetics, being convinced the Gospels and New Testament are true, and personal revelation. Again, many people forget that the word has been hijacked to mean believe without reason, or what is colloquially called blind faith. The word simply does not mean that and that phrase and the actually definition of faith are contradictory. In short, faith means believing in what you have reason to believe.

So the phrase the science of faith means exactly knowledge of what there is reason to believe. Specifically, in this context, the author means exclusively items concerning Christianity and the Christian God. So alternatively, the author may mean knowledge of the Christian religion with assumptions that it is true at its core. Slightly different than what I have come up with, but acceptable and understandable considering the time and place that he said that.


Has the Catholic Church endorsed the view of Einstein on the Creator?

Catholicism believes in a personal God - a rational being who loves, creates as a voluntary act, and cares for His creation. Einstein found himself unable to believe in such a God:

  "It seems to me that the idea of a personal God is an anthropological concept which I cannot take seriously."
  (letter quoted in  Hoffmann, Banesh: Albert Einstein Creator and Rebel. Cited in the Wikipedia article "Religious and philosophical views of Albert Einstein.)

When Einstein used the word "God" in the quote you cite, therefore, he seems to have meant something very different than what the Church means. So it would be surprising if the Church used the statement at all in any teaching.

That said, the Church certainly believes that God, in its use of the word, "does not play dice with the universe" - that is, he does not allow things to happen which are not beyond his ultimate control. The Church believes that all things occur subject to Divine Providence; they are all part of (or incorporated into) God's Divine Plan for the universe. Even physical events which seem random are part of what God wills for the universe:

  God does not abandon his creatures to themselves. He not only gives them being and existence, but also, and at every moment, upholds and sustains them in being, enables them to act and brings them to their final end.
  Catechism of the Catholic Church, paragraph 301

Thus, although the Church rejects what Einstein said of God, in that it rejects his understanding of God, She still teaches something similar regarding God as He is in truth.


What are some countries where you can be imprisoned for reading or owning a Bible?

Countries which ban the possession of the bible include:

Saudi Arabia

  At present, the Bible has been banned in Saudi Arabia. In a number of countries, bible translation, distribution, sale or promotion is prohibited or made difficult, and the Bible may be considered extremist materials. Historically, some countries banned the Bible in certain languages or versions. The Bible in Spanish was prohibited in Spain from the sixteenth until the nineteenth century. In 1234, King James I of Aragon ordered the burning of Bibles in the vernacular. In 2015, Russia banned import of the Jehovah's Witnesses' New World Translation of the Holy Scriptures. - List of books banned by governments

North Korea

  People found with Christian Bibles, which are considered to be a symbol of the west can be executed or tortured. Refugees and defectors continued to allege that they witnessed the arrests and execution of members of underground Christian churches by the regime in prior years. Due to the country's inaccessibility and the inability to gain timely information, this activity remains difficult to verify. - Freedom of religion in North Korea

More on North Korea:

  In this totalitarian state, the only thing that North Koreans are permitted to worship is the nation's leader, Kim Jong-un. Bibles are banned and those found in possession of one, face imprisonment, torture and even death – as do up to three generations of their family. - Source

Somalia

  Christians residing in Somalia face constant persecution from radical Islamists and government officials. The prevalence of the Islamic extremist group, al-Shabaab means that believers often practise their faith in extreme secrecy and cannot own Bibles. - Source

Maldives

  The Maldives have a reputation for being a luxurious idyll but a Bible can get you into trouble in this paradise. Under the country's strict Islamic laws, importing a Bible is forbidden. There is currently no complete translation of the Bible into Dhivehi, the official language of the tropical nation. - Source

Morocco

  It's against the law to carry a Bible translated into Arabic in Morocco. Reports of overt Christian persecution are few but Christian children are not given a religious education. - Source

Libya

  Like Morocco, Libya has laws against bringing Bibles in the Arabic language into the country. The distribution of Bibles and evangelism is illegal. - Source

Uzbekistan

  In this Central Asian dictatorship, high penalties are imposed on those who own Bibles. Authorities are known to detain Christians found in possession of the holy book for "keeping and storing extremist materials with the purpose of further distribution." - Source

Christian Persecution On The Rise In Uzbekistan Where Just Owning A Bible Is Illegal

Open Doors profiles annually 50 countries “where Christians face the most extreme persecution.”


What can be said when applying ashes during Ash Wednesday Mass?

The website liturgies.net appears to have a full copy of the Roman Missal, including the propers of the Mass for Ash Wednesday. This states:

  [The priest] sprinkles the ashes with holy water, without saying anything.

  Then the Priest places ashes on the head of all those present who come to him, and says to each one:

  Paenitemini, et credite Evangelion.
  Repent, and believe in the Gospel.

  Or:

  Memento, homo, quia pulvis es, et in pulverem reverteris.
  Remember that you are dust, and to dust you shall return.

I am attempting to find where in the Missal the statement originates.


What was the concept of heaven people had before the death of Jesus?

The following is the closest I am able to find in trying to answer your question from a Catholic perspective.

As to what the Chosen People actually believe today may be something totally different. Remember that the Sadducees of Christ’s day and age denied the resurrection.

Religion historian Philip Jenkins believes the books of Wisdom and Maccabees can explain the origins of Christian beliefs about heaven and hell. His article is found on U.S.Catholic (Faith in Real Life).

  What early Christians learned from Jews about the afterlife

  Historically, there are many reasons why different religious bodies defined their scriptures as they did, but Catholics should be very grateful to have the texts they do. Far from being marginal or apocryphal, texts like Wisdom and Maccabees are precious testimony to a revolutionary era in Jewish history—roughly, the three centuries or so before Jesus’ time, a period that shaped emerging Christianity.

  When we read these often under-appreciated books today, we encounter ideas and beliefs that were quite startling at the time but that formed the outlook of Jesus’ first followers. These writings allow ordinary believers today an unparalleled glimpse into the thought world of the early Christian community. Moreover, these books demonstrate the continuity between the Jewish world and later Christian—and, specifically, Catholic—faith and practice, especially in changing attitudes toward the afterlife and of heaven, hell, and judgment.

  Throughout the gospels Jesus often speaks of the future life, of the fates reserved for the virtuous and the wicked. Not every Jew at the time shared those views, and the influential faction of the Sadducees even denied the afterlife. Even so, the early Christians were firmly rooted in the Jewish beliefs of the time: Death was assuredly not the end.

  But the more we investigate the Hebrew Bible, the more surprised we should be by this fact. Through most of the early history of the Hebrew people, the afterlife was anything but an obvious or accepted doctrine, and only in the three centuries or so before Jesus’ time did that situation change. Those centuries mark a tectonic shift in religious thought, and Jesus’ followers were at its heart. Both the books of Wisdom and Maccabees served as key manifestos for that revolution.

  When Old Testament books and authors discuss the afterlife, the picture they present is anything but hopeful. Before the sixth century BCE individuals who died survived at best as shades who had little distinct identity. In the grim words of Psalm 115, “The dead do not praise the Lord, nor do any that go down into silence.”

  The Bible refers often to Sheol, the place of the dead, but this miserable place was not reserved for notorious sinners or wrongdoers. Regardless of your goodness or piety, the ultimate fate of humanity was the grave with its maggots and worms. In the third century BCE the author of Ecclesiastes wrote that the same fate ultimately comes to righteous and evil alike. All go down to Sheol. “But whoever is joined with all the living has hope, for a living dog is better than a dead lion. The living know that they will die, but the dead know nothing; they have no more reward, and even the memory of them is lost” (Eccl: 9:4–5). Only the fact that the book was credited to King Solomon ensured that such a materialist manifesto remained within the biblical canon.

  Later readers, Jewish and Christian, can point to some passages as indicating a belief in survival or resurrection, such as Ezekiel’s story of the valley of dry bones (37:1–14). Usually, though, such texts are visions of a collective future resurrection of the Hebrew people rather than of any given individual.

  So what changed? Jewish beliefs were first transformed at the time of the Exile to Babylon in the sixth century BCE, and ideas of an afterlife become much more obvious in so-called post-Exilic works written after the 520s.

  The main reason for change was the increasingly firm monotheism taught originally by the great prophets. They rejected any suggestion that the God of Israel had consorts or companions and scoffed at images of God sitting in a heavenly court with fellow deities and goddess wives. Nor was God the lord of the Hebrew nation alone while other divine figures ruled only their particular peoples. For prophets like Isaiah or Jeremiah God was absolutely and sternly alone, the one creator and Lord of the whole earth.

  But that strict monotheism raised troubling questions, especially about the nature of good and evil. If God was alone and all-powerful, then his followers had to explain the existence of so much evil in the world. Why did so many evildoers end their days in comfort and security, while the righteous perished in gutters?

  While believers used many strategies to address those questions, the idea of the afterlife helped enormously. If wrongdoers flourished today, they would get their comeuppance in another life when the virtuous and poor would receive their rewards. One great meditation on those issues of ultimate justice is the Book of Job, which was probably written in the fifth or fourth century BCE, and which includes a stunning suggestion of future resurrection.

  Afterlife beliefs became much more popular and widespread from the third century BCE onward, when ideas of heaven, hell, and resurrection were freely discussed in highly influential writings that are not included in most canonical Bibles. The most important was the first Book of Enoch, which Jesus certainly knew and which early Christians regarded as inspired scripture.

  The text as we have it combines several separate writings created at various points between about 250 and 100 BCE. Throughout Enoch we find stories of heavens and hells, each presided over by archangels and devils in a way that looks utterly familiar to modern readers but which was daring and innovative in its age. The book’s readers hoped for heaven and feared hell.

  One critical event fanned the flames of otherworldly expectation, namely the great Maccabean revolt of the 160s BCE, when faithful Jews rose in armed rebellion against pagan Greek overlords. The ensuing wars were savage, and countless Jewish patriots were killed, often in circumstances of vicious torture and persecution.

  Again the question arose: Did these individuals really have no hope of reward or vindication beyond the collective good of the Hebrew people? But of course they did, if you assumed an individual afterlife and a resurrection to judgment. Back in the fourth century a glorious afterlife was a distant aspiration; by the second the idea became an urgent necessity.

  We see the shift in attitudes in the book called 2 Maccabees, which Catholics and Orthodox Christians accept as a fully canonical part of scripture, but which Protestants see as apocryphal. Probably written in the late second century BCE, the most astonishing thing about 2 Maccabees is that so little in it surprises us today. Throughout, we read stories that exactly fit our expectations of how God’s martyrs should behave.

  When one resistance hero has his hands severed, he declares that he will receive them again after his death. His brother proclaims a similar faith and warns his persecutors that they, unlike he, will have no resurrection which they can look forward.

  Writers of the post-Maccabean era explored the possible implications of that core idea of survival after death, and some of the beliefs they report sound as if they belong to a much later era, to the point of prefiguring a Christian thought-world. After the great nationalist hero Judah the Maccabee secured victory, 2 Maccabees reports how he collects money to be sent to the Temple for a sin-offering for those who had fallen in heroic battle.

  The author holds out this deed as an example for others to follow: “For if he were not expecting that those who had fallen would rise again, it would have been superfluous and foolish to pray for the dead. . . Therefore he made atonement for the dead, so that they might be delivered from their sin” (2 Macc. 12:44–45). The doctrines expressed here sound oddly akin to ideas of later Catholic Christianity, including the communion of saints and the practice of prayer for the dead.

  For most Jews the afterlife became a natural expectation. That change is obvious in the Book of Wisdom that Christians find in their own Bibles, and which dates to the first century BCE. Wisdom offers a telling parody of the Ecclesiastes text quoted above—ironically, because like Ecclesiastes this text too is credited to King Solomon. As the author of Wisdom asks, so you believe that we are shadows that just fade away, and nobody returns after death? So what is to prevent you from committing every form of sin and exploitation? In reality, says Wisdom,

    The souls of the righteous are in the hand of God,
    and no torment will ever touch them.
    In the eyes of the foolish they seemed to have died,
    and their departure was thought to be affliction disaster,

    and their going from us to be their destruction;
    but they are at peace. . . .
    Having been disciplined a little, they will receive great good,
    because God tested them and found them worthy of himself;
    like gold in the furnace he tried them,
    and like a sacrificial burnt offering he accepted them. (3:1–6)

  Not surprisingly, this is a popular text at modern Christian funerals, where these comforting words seem familiar and appropriate. But how radical were these ideas compared to what had gone before in the Hebrew tradition! So beautifully did Wisdom expound later Christian ideas that some early churches wanted to include it in the New Testament, rather than the Old.

  In the century or so before Jesus was born the afterlife theme was freely discussed in many once-beloved texts and tracts, and Jesus and his first followers certainly knew most of them. (They were not included in any later Bibles.)

  The Testament of Judah tells us how “they who have died in grief shall arise in joy, and they who have lived in poverty for the Lord’s sake shall be made rich, and they who have been in want shall be filled, and they who have been weak shall be made strong, and they who have been put to death for the Lord’s sake shall awake in life.” Those assurances about future rewards sound very close to the beatitudes of Jesus himself, who was likely recalling the text.

  No one source or writing carried those doctrines of the afterlife into the apostolic world. Rather, the ideas had become standard in the Jewish world in the previous few generations, and they became the familiar subject matter of many writings. What impresses us today is how firmly the early church was building on those Jewish precedents, including some ideas that we might have thought much later. Nothing better illustrates the thoroughly Jewish setting from which Jesus and his first followers emerged.

  There are many reasons to read and reread books like Wisdom and 2 Maccabees. You can read them as historic documents, or they can serve as mighty defenses against those who believe that Catholic doctrines such as prayer for the dead are unscriptural. Above all. they are magnificent statements of core Christian doctrines and wonderful expositions of that faith. - What early Christians learned from Jews about the afterlife


What is the nature of Dyothelitism according to the Council of Chalcedon?

The Definition produced by the Council of Chalcedon in 451 is an interesting text because it wasn't intended to stand alone; it was produced by people who knew well that they were part of a series of church councils stretching back over a century. So the Chalcedonian Definition endorses the 325 Nicene Creed, and it's 381 Constantinopolitan revision, as well as endorsing the 431 Council of Ephesus. This last council forbade any departures from the Nicene Creed, and so the Council of Chalcedon was careful not to say that it was producing a new creed, but instead a definition or statement that merely clarified the Nicene Creed. The Council of Chalcedon was called in order to unite a divided Christendom, so in addition to endorsing the previous Creeds, it also endorsed the letters of Cyril of Alexandria and the Tome of (Pope) Leo, in order to bring together the three major camps of Christianity of the era: Western, Antiochene, and Alexandrian.
The Tome of Leo is of particular interest to this question because it gives great clarity to the Chalcedonian Definition in a way that I hope will answer your questions. This is the relevant section:

There is nothing unreal about this oneness, since both the lowliness of the man and the grandeur of the divinity are in mutual relation. As God is not changed by showing mercy, neither is humanity devoured by the dignity received. The activity of each form is what is proper to it in communion with the other: that is, the Word performs what belongs to the Word, and the flesh accomplishes what belongs to the flesh. One of these performs brilliant miracles; the other sustains acts of violence. [EWTN]

The Tome of Leo rules out monothelitism because rather than each nature acting and performing what is proper to itself, the divine will would be acting for both the divine and human. (Note that mono-/dyothelitism strictly refers to one/two wills, but the theological principles that lead us to understand that Christ had two wills apply equally to the mind.)
So on to your questions.

What is the relationship of the divine mind with the human mind?

So from the Chalcedonian Definition we understand that, as they are faculties of the natures, they must be "unconfused, unchanged, undivided, inseparable". From the Tome of Leo, we know that each nature exercises its faculties in communion with the other. And from the Third Council of Constantinople (which rejected monothelitism), we get a clearer picture of just how the two natures relate in general:

And the two natural wills not in opposition, as the impious heretics said, far from it, but his human will following, and not resisting or struggling, rather in fact subject to his divine and all powerful will. (Source)

When Jesus was incarnated, did he use his human mind primarily?
Was Jesus operating in both human mind and divine mind simultaneously when he was on earth?

The person we call Jesus is the Son of God who exists now in two natures, so we mustn't make the mistake of saying that "Jesus" refers just to the human nature. So the answer to question 2 is no and the answer to question 4 is yes: Jesus didn't primarily use his human mind; his divine nature thought exclusively with his divine mind, and his human nature thought exclusively with his human mind, both natures were united and acting together. Even if we think of the human mind as following and submitting to the divine mind, we cannot think of him therefore predominantly using his divine mind. Jesus was not a comatose body animated by the divine mind of God, but a complete living human who was the incarnate Son of God.

If so, how did Jesus access his divine mind? Is it like a memory being remembered?

I think this is where any answer will get more speculative, for I don't think the mechanisms of the communion of the two natures has been revealed to us with any great clarity. But there are several instances in the Gospels which show us some of the ways in which his natures worked together.
Several times the Gospels say that Jesus knew what other people were thinking (Matthew 9:4, 12:25, Luke 6:8, 9:47, 11:17). This kind of knowledge is outside the capabilities of a human, and so in these times we see, somehow, the communication of knowledge from the divine mind to the human mind.
There is at least one major case where the divine mind's knowledge is kept from Christ's human mind: the time of his return (Matthew 24:36, Mark 13:32). More on that at this question/answer.
Another interesting case is when Jesus healed the woman who had been bleeding for twelve years (Matthew 9:20-22, Mark 5:25-34, Luke 8:43-48). I think his question "Who touched me?" is usually thought of as a rhetorical question, but is that necessarily true? Mark says Jesus "kept looking around" and Luke has Jesus quite adamantly respond to Peter that he knew he had been touched and power had gone out from him. I think it would be better to read this not as a rhetorical question from Christ's human nature which had been given omniscience by his divine nature, but instead the genuine question of a human man who for whatever reason was not at this time being given insight from his divine nature.
Lastly are the times when the human nature of Christ expressed emotions that are foreign to the divine nature: exhaustion (John 4:6), grief (John 11:33-35), anxiety and dread (Matthew 26:36-39, Luke 22:40-44). Perhaps even frustration (Matthew 16:5-11), if we think of the divine nature as having unlimited patience. In all of these times the divine nature could have intervened, to re-energise his human nature, to give comfort, to give patience. And no doubt the divine nature did just that at many times to various extents, but in these times the human nature was seemingly left without divine intervention to experience the troubles of human existence which he shares with us. But we must not think of the natures acting in discordance even in these times: even these times when divine power was not communicated to the human nature were times when the two natures of Christ were operating together with singular purpose, no doubt to reassure us that he can be our high priest because he is truly one of us (Hebrews 2:17-18.)


What is the biblical meaning of "sanctification"?

The word "sanctification" derives from the Latin noun "sanctificio".  This original Latin word means "to separate and set aside" (source--using the WayBack Machine).

To me, this rings of Isreal being set aside as God's holy people. (As seen in Deut. 7:6-8 and Leviticus 20:26)   Also, it seems to reverberate in the New Testament with Jesus' words in the gospel of John.

John 17:16 (NIV)

  16 They are not of the world, even as I am not of it.

Sanctification, in this sense, is to be set apart from the world--to be a different people.

However, this original Latin word was actually translated from Greek.  It's not actually the source word.  The original Greek word is often translated into English as "wash" or "cleanse".

This implies that we are to be washed of our sins.

There's an excellent use of this in Ephisians 5:25-26.  The NIV translates this as "cleanse"

Ephisians 5:25-26 (NIV)

  25 Husbands, love your wives, just as Christ loved the church and gave
  himself up for her 26 to make her holy, cleansing her by the
  washing with water through the word

(emphasis added)

However, the original King James uses the word "sanctify"

Ephisians 5:25-26 (KJV)

  25 Husbands, love your wives, even as Christ also loved the church, and gave himself for it;

  26 That he might sanctify and cleanse it with the washing of water by the word

(emphasis added)

This cleansing from sin can also be seen in the Old Testamant.

Leviticus 16:30 (KJV)

  30 For on that day shall the priest make an atonement for you, to
  cleanse you, that ye may be clean from all your sins before the LORD.

It should be noted, though, that the translation of "sanctify" in the Old Testament didn't suffer from this same duality of definition.  It's just an example of how God's holy people should be both "set apart" and "cleansed".

So, there is kind of a two-fold definition.  My source article puts it well:

  In position believers are eternally set apart for God by redemption and are positionally, therefore, holy and righteous from the moment of believing.
  In experience the believer is being sanctified by the work of the Holy Spirit and scripture.

(emphasis in the original)


Is it possible for an Eastern Rite Catholic to change over to the Roman Rite and become ordained as Latin Rite priest?

There has been long-standing tradition of Syrian Catholics of Kerala, Southern India getting ordained as parish priests of churches belonging  to Latin Rite dioceses and  some of them even becoming Bishops of the dioceses within the Roman Rite.


Why did Elizabeth keep herself hidden while pregnant?

Note that she waited only for five months, not the full term. I'd speculate that perhaps her history of barrenness was full of miscarriages, and she wanted to be confident that she would carry this baby to term.

Calvin offers two alternate possibilities as to why:

  There might be two reasons for the delay. Until this extraordinary work of God was manifest, she might hesitate to expose it to the diversified opinions of men, for the world frequently indulges in light, rash, and irreverent talking about the works of God. Another reason might be that, when she was all at once discovered to be pregnant, men might be more powerfully excited to praise God.† It was not, therefore, on her own account, but rather with a view to others, that Elisabeth hid herself.

† This is from the Latin version. Calvin's French version says, "For, when the works of God show themselves gradually, in process of time we make less account of them than if the thing had been accomplished all at once, without our having ever heard of it."