Does the Catholic Church attempt to explain scientifically any miracles associated with Jesus' time on earth?
I know of no Catholic theologian or Catholic scientist who has attempted to do so with the Biblical miracles performed by Christ.
But it is certainly permitted within the philosophical understandings of the Catholic Church. Just because I do not know of anyone within the Church to have done so: yet.
To be honest here, I would be surprised that no Catholic theologian or scientist has taken up this avenue of research. Just can not find one...
It could stated here that the miracles needed for a beatification or canonization are done by the power of God and by extension Christ who is the Second Person of the Most Holy Trinity.
Revelation 5:8 speaks of 24 elders with golden bowls full of incense, which are the prayers of the saints, but Catholics are not as wedded to the text of Scripture as in other denominations. It is a long tradition, that some Protestants would argue is not unbiblical, that deceased Christians pray for and can even, through the power of God, work miracles for, the living.
Pope St. John Paul II’s encyclical letter Fides et Ratio gives the faithful a way to understand scientific research in the domain of faith, when trying to understand the Mysteries of Faith such as the Resurrection of Christ. Scientific research into the miracles of Jesus must follow clear guidelines in order to remain valid forms of research and investigation.

It may help, then, to turn briefly to the different modes of truth. Most of them depend upon immediate evidence or are confirmed by experimentation. This is the mode of truth proper to everyday life and to scientific research. At another level we find philosophical truth, attained by means of the speculative powers of the human intellect. Finally, there are religious truths which are to some degree grounded in philosophy, and which we find in the answers which the different religious traditions offer to the ultimate questions. (30)
The more influential of these radical positions are well known and high in profile, especially in the history of the West. It is not too much to claim that the development of a good part of modern philosophy has seen it move further and further away from Christian Revelation, to the point of setting itself quite explicitly in opposition. This process reached its apogee in the last century. Some representatives of idealism sought in various ways to transform faith and its contents, even the mystery of the Death and Resurrection of Jesus, into dialectical structures which could be grasped by reason. Opposed to this kind of thinking were various forms of atheistic humanism, expressed in philosophical terms, which regarded faith as alienating and damaging to the development of a full rationality. They did not hesitate to present themselves as new religions serving as a basis for projects which, on the political and social plane, gave rise to totalitarian systems which have been disastrous for humanity. (46)
In the field of scientific research, a positivistic mentality took hold which not only abandoned the Christian vision of the world, but more especially rejected every appeal to a metaphysical or moral vision. It follows that certain scientists, lacking any ethical point of reference, are in danger of putting at the centre of their concerns something other than the human person and the entirety of the person's life. Further still, some of these, sensing the opportunities of technological progress, seem to succumb not only to a market-based logic, but also to the temptation of a quasi-divine power over nature and even over the human being. (46)
Finally, I cannot fail to address a word to scientists, whose research offers an ever greater knowledge of the universe as a whole and of the incredibly rich array of its component parts, animate and inanimate, with their complex atomic and molecular structures. So far has science come, especially in this century, that its achievements never cease to amaze us. In expressing my admiration and in offering encouragement to these brave pioneers of scientific research, to whom humanity owes so much of its current development, I would urge them to continue their efforts without ever abandoning the sapiential horizon within which scientific and technological achievements are wedded to the philosophical and ethical values which are the distinctive and indelible mark of the human person. Scientists are well aware that “the search for truth, even when it concerns a finite reality of the world or of man, is never-ending, but always points beyond to something higher than the immediate object of study, to the questions which give access to Mystery”. (106)

The miracles performed by Christ, like the miracles needed in the cases of beatification and canonization
are events that go beyond the forces of nature, which are realized by God outside of what is normal in the whole of created nature.

"For the beatification of a servant of God who is not a martyr, the Church requires a miracle; for canonization, including that of a martyr, it requires another," he explained. "Only the presumed miracles attributed to the intercession of a servant of God or of a blessed 'post mortem' can be the object of verification."
A miracle is an "event that goes beyond the forces of nature, which is realized by God outside of what is normal in the whole of created nature by the intercession of a servant of God or a blessed," Monsignor Di Ruberto said.
The investigation of a miracle is carried out separately from that of virtues or martyrdom.
Consequently, the recognition of a miracle "makes it possible to grant with certainty permission for devotion," he added. Hence, the "capital importance of keeping miracles as a requirement in the causes of canonization."
A collegial body made up of five medical specialists and two professional experts form the Medical Consultation, in charge of the scientific examination of the presumed miracle. Their judgment is of a "strictly scientific" character, so their being "atheists or of other religions is not relevant," Monsignor Di Ruberto emphasized.
"Their examination and final discussion are concluded by precisely establishing the diagnosis of the illness, the prognosis, the treatment and its solution," he continued. "To be considered the object of a possible miracle, the cure must be judged by the specialists to have been rapid, complete, lasting and inexplicable, according to present medical-scientific knowledge."
The miracle might go beyond the capacities of nature in regard to the substance or the subject of the event, or the way it occurred.
So a distinction is made of three great miracles: the resurrection of the dead; the complete cure — which might entail the reconstruction of organs — of a person judged incurable; or the curing of an illness — which could be cured over time but takes place instantly.
"If there are uncertainties, the consultation suspends the evaluation and asks for more experts or documentation," Monsignor Di Ruberto said. "Once there is a majority or unanimity in the voting, the examination is sent to the theologians' consultation."
Starting with the conclusions of the Medical Consultation, the theologians "are called to identify the nexus of causality between prayer to the Servant of God and an inexplicable cure or technical success, and they express the judgment that the prodigious event is a real miracle."
"When the theologians have also expressed their vote in writing, the assessment is sent to the Congregation for Bishops and cardinals who, after hearing the exposé of a 'speaker,' discuss all the elements of the miracle," the monsignor said. "Each component, therefore, gives his judgment, which must be submitted for the approval of the Pope."
Finally, it is the Holy Father who "determines the miracle and decides on the promulgation of the decree," the monsignor said. The latter is a juridical act of the Congregation for Sainthood Causes, sanctioned by the Pope, "by which a prodigious event is defined as a genuine miracle," he concluded. - Why Miracles Are Required for Canonizations

Scientific research into the Biblical miracles performed by Jesus should have as as an object to gain deeper and more clear understanding of Christ’s life and works while amongst men. It is not a question of trying to draw doubt one these issues. This remains a viable and valid form of genuine Catholic scientific research by Catholics researchers of the truths within our holy religion. Truth has nothing to fear.
The following articles may be of interest to some:

Miracles of Christ: They may be divided into five classes: nature miracles; miracles of healing; deliverance of demoniacs; victories over hostile wills; cases of resurrection.
Does It Make Sense To Believe Saints Can Work Miracles?


Any radical transformation in case of incarnation without fall?

The answer is Yes according to Eastern Church Fathers as they teaches the word Theosis.

  Theosis, or divinization ("divinization may also refer to apotheosis, lit. "making divine"), is a transformative process whose aim is likeness to or union with God, as taught by the Eastern Orthodox Church and Eastern Catholic Churches. As a process of transformation, theosis is brought about by the effects of catharsis (purification of mind and body) and theoria ('illumination' with the 'vision' of God). According to Eastern Christian teaching, theosis is very much the purpose of human life. It is considered achievable only through a synergy (or cooperation) between human activity and God's uncreated energies (or operations).[1]https://en.wikipedia.org/wiki/Theosis_(Eastern_Christian_theology)

Adam & Eve have access to the Tree of Life, and the fruit of the Tree of Life is what the Catholic Church believe today as the Holy Eucharist. The transformation, the Catholic Church teaches is a "transfigured bodies" for those who lived a Eucharistic Life.

  Saint Albert the Great taught that the Eucharist, the Body and Blood of Christ, is the Fruit of the Tree of Life.https://en.wikipedia.org/wiki/Tree_of_life

  1000 This "how" exceeds our imagination and understanding; it is accessible only to faith. Yet our participation in the Eucharist already gives us a foretaste of Christ's transfiguration of our bodies:

  Just as bread that comes from the earth, after God's blessing has been invoked upon it, is no longer ordinary bread, but Eucharist, formed of two things, the one earthly and the other heavenly: so too our bodies, which partake of the Eucharist, are no longer corruptible, but possess the hope of resurrection.556

Question: How it would be possible to lay down one's life for one's friends if there is no death?

If Adam & Eve did not Fall then Jesus would still come as Creation & Incarnation is not a separate plan but a complete plan of God based on the teaching of Blessed John Duns Scotus on the Primacy of Christ. According to Blessed Scotus Jesus will still come not as a Redeemer but King of His creation.

  The theology of John Duns Scotus places Christ at the centre of a universe ordered by love. Christ is presented as the basis of all nature, grace and glory – the most perfect model of humanity. He is at the beginning, the centre and the end of the universe.

  St. Paul tells us that Christ was the first-born of all creation, and Scotus’ theology makes sense of this affirmation. Scotus did not believe that the acts of creation and Incarnation were separate, but part of one divine plan. So rather than the Incarnation being a sort of “Plan B” to rescue humanity after the fall, in Scotus’ theology it is the whole purpose of creation. Christ is the masterpiece of love in the midst of a creation designed for love, rather than a divine plumber come to fix the mess of original sin. Thus the Incarnation is placed by Scotus in the context of creation and not of human sin.
  The Primacy of Christ in John Duns Scotus: An Assessment.

Note: I heard somewhere that there would be some transition like this, just without sorrow and pain. Similar to Mary's assumption. How it would look like? Would the person after the transition still be on the Earth?

This is a different scenario on your premise above wherein Adam  Eve did not Fall. Mary's Assumptions happened because original sin enters the world. You might probably asking on the appearance of the faithful souls in the New Paradise. The Book of Revelation speaks of a Eucharistic Era, so based on Catholic Church Catechism#1000 souls will be given a foretaste of Christ "transfigured bodies".

In closing,the Primacy of Christ teaches that the Omnipotent God in all eternity knew that Adam & Eve will fall into temptation even the Fall of Lucifer as the Wisdom of God knew everything.

  "For the spirit of the Lord fills the world,
      is all-embracing, and knows whatever is said.(Wisdom1:7)

The Primacy of Christ is the ultimate radical transformation, A
Creator transforming into a creature assuming humanity devoid of all powers  majesty, but why?

St.Athansius has the answer;

  "God becomes man, so that man shall become gods."(St.Athanasius)

Jesus the Begotten Son of God has to come down to show us the Way how to enter His Father's Kingdom, and there's is only one way and the first one who teach the Apostles the Way that Jesus had shown by His life is the Theotokos. The Catholic Church teaches that the Way to Heaven and "transformation" is the Way of the Cross.

As St.Paul boldly exclaimed his own transformation;

  "I have been crucified with Christ, and I no longer live, but Christ lives in me. The life I live in the body, I live by faith in the Son of God, who loved me and gave Himself up for me. (Galatians2:20)


Is there any denomination which teaches that God never commanded burnt offerings and sacrifice to Israel?

No, not really. The closest we get is the Marcionites, a Gnostic sect who rejected the Old Testament and believed the God of the Israelites was a different and inferior god to the god of the New Testament.

Nevertheless, this question would never rise or fall on the translation of Jeremiah 7:22 since there are tons of extended passages in the Old Testament where God does prescribe burnt offerings and sacrifices.

The ESV translation is getting at the fact that God is mainly angry that his voice has not been heeded, not that he hasn't had enough sacrifices. His evidence is that when the Israelites came out of Egypt, he didn't give them any instruction about sacrifices until they made it to Siani. His only requirement was that they would follow his voice and obey him.


What does childbearing have to do with the salvation of a woman?

As timf quoted:

  they will be saved [eternally] if they continue in faith and love and holiness with self-control, [saved indeed] through the Childbearing or by the birth of the divine Child. - Amplified

Childbearing resulted in the birth of Jesus.
If you look at "she", the "woman" as an image not for each woman as an individual, but as womanhood as a whole, or as Eve specifically, who is mentioned in the verse before, than she, the woman is saved through childbearing - the birth of Jesus.
Or as you can already see promised in Genesis 3, when God addresses the snake:

  And I will put enmity
      between you and the woman,
      and between your offspring and hers;
  he will crush your head,
      and you will strike his heel - Genesis 3:15.

Eve's offspring - singular - will crush the snake's head and destroy it.

Now that still leaves the part of the verse where it says "if they continue in faith and charity and holiness with sobriety" ... and that may still sound like this salvation requires works. However notice what it mentions first in this list after childbearing, which as explained refers to Jesus: faith. This faith and resulting life change then results in charity and holiness and sobriety - which are things God does works in us through His Holy Spirit - see for example Gal. 5:22-23.


I think what you are seeing is a reaction to a stereotype created by our culture and the popular media.  Much like the picture in the minds of many people of the Devil parading around in red tights with a pitch fork.

In actual fact, scripture teaches us that Lucifer, whose name means "Light Bearer", was the "Morning Star" who fell from heaven in Isa 14 and Ezekiel 28 describes him as "the seal of perfection, Full of wisdom and perfect in beauty".  He is understood to have been an archangel and a prince of heavenly worship.  Other scripture teaches that he comes as an "angel of light" (2 Cor 11:14).

So, in actual fact, the devil is likely to present as someone visually and audibly beautiful.  Some allowance may need to be made for subsequent corruption after he fell, but since angels are purely spiritual beings, they likely can manifest in our realm in any form that serves their purpose.

Now, while I personally don't care for grungy metal and don't find it either pleasing or uplifting, I find it unlikely that it's inherently demonic simply because it uses raspy metallic vocals.


What's the name of the process by which the scriptures were written down?

Concursus is a Latin word which can be translated encounter or meeting. The late 19th–early 20th century Presbyterian theologian Benjamin Breckenridge Warfield used the word to describe his belief that

  the whole of Scripture is the product of the divine activities which enter it, not by superseding the activities of the human authors, but by working confluently with them, so that the Scriptures are the joint product of divine and human activities, both of which penetrate them at every point, working harmoniously together to the production of a writing which is not divine here and human there, but at once divine and human in every part, every word and every particular.

(source: B. B. Warfield, "The Divine and Human in the Bible," in Selected Shorter Writings of Benjamin B. Warfield (ed. John E . Meeter; Presbyterian and Reformed, 1970), page 57. Cited on a web page at The Biologos Forum. Here is a copy of the original essay, discussing concursus and its meaning.)

Thus, concursus doesn't describe "the process by which the Scriptures were written down" generally, but rather one theologian's view of the interaction between God and the humans who wrote down the Scriptures.


How do I track the history of changes to a given verse's actual text? How do I discover it's "lineage"?

The type of work you are looking for is called an apparatus, such as Bruce Metzger's Textual Commentary on the Greek New Testament which explains the choices made in compiling the UBS4 Nestle-Aland 27 (one of the best Greek texts, pulling together most of the known codexes, manuscripts, and papyri out here)

When using an apparatus, you should become familiar with the distinction between the texts (Say, codex Sinaiticus, an aleph, vs. Codex Vaticanus, a B, what a papyri is, what an Mss. Is, etc.) This link, a guide to the critical apparatus of the BHS (Biblica Hebraica Stugartensia) does a pretty good job of explaining the approach that scholars use in determining the lineage of a text.

It will talk about what manuscripts inform the current text out there, and it will discuss why a particular variant should be chosen. Additionally, it grades the certainty with which the scholars believe it to be "original".
This link is not comprehensive, but gives an excellent overview of some of the more problemmatic variants. An example variant would be described as such:

  2 John 12:

  TEXT: "so that our joy may be made full"

  EVIDENCE: S K L P Psi 104 614 630 945 2495 Byz Lect syr(ph,h)
  TRANSLATIONS: KJV RSV NASVn NIV NEB TEV
  RANK: C

  NOTES: "so that your joy may be made full"

  EVIDENCE: A B 33 81 1739 1881 lat vg cop(north)
  TRANSLATIONS: ASV NASV

  OTHER: "so that my joy may be made full"

  EVIDENCE: cop(south)

  COMMENTS: In later Greek the words for "our" and "plyour" were pronounced alike. It is likely that copyists misheard "our" as "your," influenced by the two previous occurrences of "you" in the verse.

In this instance, particular attention should be paid to the "Evidence" entry.  Each letter or abbreviation refers to a particular manuscript that contains the variant.

Finally, if you check out the Net Bible, their public domain text has incorporated the apparatus into the footnotes in most places where there is any question. For example:

  3 tc ‡ Most witnesses ([א] A P 1739 Ï sy) have καί (kai, “also”) before the article τόν (ton). But the external evidence for the shorter reading is significant (B Ψ 048vid 33 pc sa), and the conjunction looks to be a motivated reading in which scribes emulated the wording of 4:21 (ἀγαπᾷ καὶ τόν, agapa kai ton). NA27 places the conjunction in brackets, indicating doubts as to its authenticity.

Again, notice the 'most witnesses' and the list of manuscripts.  The 'A' representing Tischendorf's stolen Codex Sinaiticus is properly called א in this work.


What does being lukewarm mean in contrast with being hot or cold for the church of Laodicea?

In addition to what was said before hot and cold being opposites one a passionate for God and another being cool. Both hot and warm water were considered luxuries during the days in which the epistles were written and both had positive qualities. Stagnant lukewarm water however had a special meaning to the Laodicean's as is related in the following explanation from March 5 2013 Sparking Gem From the Greek by Rick Renner:

The city of Laodicea was built in a region that was full of seismic activity and had experienced many earthquakes. As often happens in a seismic area, vents came up from the depths of the earth, allowing boiling hot water to reach the surface. In the nearby city of Hierapolis, these hot springs were famous. People came from great distances to bathe in those waters, believing they had medicinal powers. An experience in those waters was viewed to be therapeutic and effective in improving one's health.
Another city named Colosse was not too far away. As Hierapolis was known for its hot springs, Colosse was known for its cold waters. Just as people journeyed to Hierapolis to bathe in the hot springs for health purposes, people would travel great distances to vacation in Colosse, where they could invigorate themselves by taking frequent dips into the famous, refreshing, cool-to-freezing waters of that city.
Laodicea may have been the biggest and richest city in the area, but it had neither hot nor cold water. Therefore, the people of Laodicea had to leave their luxurious homes and travel to Colosse if they wanted to enjoy fresh, cool water. On the other hand, those who desired to soak in the hot springs had to travel six miles to Hierapolis.
Once in an attempt to bring the hot water from Hierapolis to Laodicea, a huge construction project was commenced. The goal of those who initiated the project was to build pipes that would channel the hot water six miles from Hierapolis to the city of Laodicea. The pipes effectively delivered the water - a real feat of construction at that time. Sadly, however, the water lost its heat along the way. By the time the water reached Laodicea, it was not only lukewarm, but it had developed a sickening, nauseating taste. The taste was so revolting that no one wanted to drink it!


What do Christians against state recognition of same-sex marriage think of the fourteenth amendment in US law?

There is a principle of law called "original intent".

https://en.wikipedia.org/wiki/Original_intent

Judges are supposed to rule based on what the intent was of those who wrote a law or amendment.

If you consider that no one in the 1800s considered homosexuality as anything other than an abomination not to be mentioned even if only in adult company, you would be hard pressed to see in the 14th amendment an intention to be applied to a group of what would then be considered debased criminals as most states had laws against sodomy.

There is now an overriding principle of law called, "living tree" or "throw out what you don't like".

https://en.wikipedia.org/wiki/Living_Constitution

This allows judges to discover things like a right to abortion.


What is the origin of vicars/priests wearing the white dog collar?

First of all, let us deal with the origins of the term "dog Collar".

The term "Dog Collar" is a nickname of Anglican origin  for the neckband of a clerical shirt or a Roman Collar (of the Catholic Church) in the UK.

  Dog Collar

  An Anglican nickname for the collar that accompanies a neckband shirt—it actually does look something like a flea collar, when you think about it!

Wikipedia has this to say about the "dog Collar":

  In the United Kingdom (and other British-influenced countries, such as Canada), clerical collars have been informally referred to as "dog collars"since the mid-nineteenth century. The term Roman collar is equivalent to "clerical collar" and does not necessarily mean that the wearer is Roman Catholic.

The clerical collar seems to be of Protestant origin:

  Neckband Shirt

  Clergy shirts are Protestant in origin. The Rev. Dr. Donald McLeod of the Church of Scotland invented the neck-band style. (The Church of Scotland is Presbyterian.) Protestant clergy had been wearing white preaching bands for quite some time; McLeod combined them with the detachable collar that was in use at the time. The Roman Catholic Church did not adopt them as streetwear for clergy until later. They modified Rev. McLeod’s design into the tab-collar style.

This article is also interesting:

  Where did the clerical collar originate from?

  The collar has always been and still is the dress code for Protestant preachers and Lawyers in Europe. In days past, these individuals wore black and chose a white sweatband (cravat) to wear around their necks for the purpose of riding on horseback. This became personified in the UK by John Wesley, founder of the Methodists, who rode on horseback the length and breadth of England preaching the Bible. It was also the normal mode of dress for the Protestant Churches of Europe and it was not until the turn of the eighteenth century that the Catholic Church adopted it also. It was never a Roman Catholic style of clergy dress code before that time and not one picture of a Pope or member of the clergy can be seen wearing one. Sadly today most fundamentalist Protestants and particularly those from other nations erroneously think that the clerical collar is a Roman Catholic instituted style of dress code for their clergy and that Protestants should not wear it, because it represents the Roman Catholic Church, "religion" and "tradition". This type of thinking is wrong. The clerical collar is a Protestant clergy dress code.

Are there any scriptural basis for the use of a clerical collar? In this article, The true origins of  the Clerical Collar, it has a long section on the scriptural importance of the collar:

  Today, when you look at the clerical dress of the majority of religions, you will see that the leadership attire is very similar. The adaptations in headgear may be different but the style of robe and neckband are ostensibly the same. Because the Judeo-Christian faith is born out of middle eastern customs the origin of Christian clerical attire can be narrowed down to a very definite style.

  The thirty ninth chapter of the book of Exodus describes in detail how the Lord commanded Moses to make "the garments of ministry". Again in the book of Leviticus in the eight chapter and verse thirteen, tunics were brought for ministry. The most abominable thing to God is for someone to minister to Him in a secular dress code, using the system of the world's style of attire to flaunt in worship before Him. The spiritual significance of the garments, or covering, before God when conducting Worship, is of absolute importance and reverence in His presence and will affect His presence.

  For more information read the entire section on this subject: A distinct dress code is Scriptural!

A Catholic seminarian wearing a cassock with a clerical collar

  The terms “Roman collar” or “Roman shirt” refer to style, not origin. Clergy shirts are Protestant in origin. The Roman Catholic Church did not adopt them as streetwear for clergy until the 19th century.


What was written on the two stone tablets of Moses?

When the Lord finished speaking to Moses on Mount Sinai, he gave him the two tablets of the covenant law, the tablets of stone inscribed by the finger of God. (Exodus 31:18, NIV)

According to C.F. Keil there were only 172 words—the Decalogue in Exodus 20:2–17—that were written on the stones "by the finger of God." This would have easily fit.

  Nothing is said about the dimensions of the tables: at the same time, we can hardly imagine them to have been as large as the inside of the ark; for stone slab 2 1/2 cubits long and 1 1/2 cubits broad, which must necessarily have been some inches in thickness to prevent their breaking in the hand, would have required the strength of Samson to enable Moses to carry them down the mountain "in his hand" (Ex. 32:15), or even "in his two hands" (Deut. 9:15, 17). But if we suppose them to have been smaller than this, say at the most a cubit and a half long and one cubit broad, there would have been plenty of room on the four sides for the 172 words contained in the decalogue, with its threats and promises (Ex. 20:2–17), without the writing being excessively small. (Commentary on the Old Testament, by C.F. KEIL and F. DELITZSCH, 1.463-464)


Why does communion frequency vary in different denominations?

As you note, there are lots of different traditions here. My ancestry is Scottish and some old Scottish churches only celebrate communion once a year. I've looked through the some liturgies for these services that basically run all day, and it's quite an affair. I have even heard it advocated that once in a life-time ought to do the job, sort of like baptism. I don't think this is at all the spirit of the thing we find in the NT.

On the other end of the spectrum are those who say that every meal we eat together as believers counts, so basically we do it a couple times a day. For several reasons I don't think this argument holds much water.

By personal background growing up was the "traditional" once a month celebrations. I wouldn't argue that this practice is inherently wrong or sinful, but I think it is arbitrary and not the best representation of what the Lord's Supper is supposed to be about.

I believe the best representation and celebration of the Lords Supper is to do it once a week during the normal Sunday gatherings. This is consistent with the description we have of the early church gathering together (we know they did this specifically in celebration of the resurrection on the first day of each week) and the description we have of them celebrating the sacrament whenever they were gathered together.


Why do many Protestant congregations not require attendance at services on Christmas and Easter?

As far as I'm aware there's no biblical basis for requiring the church to gather at those specific times. For example there's no mention of Jesus' birth being explicitly celebrated as an occasion in Acts as far as I'm aware.

The congregation I belong to used to meet in a school as we didn't have our own building. We felt it was important to give the school caretakers a break at these times, so our church didn't meet during the school holidays (although we were encouraged to visit other churches or arrange other activities).


Why did Jesus say to his accusers "You are gods"?

Here is one of those times where context helps quite a bit.

  John 10:33-36 (NIV)

   33 “We are not stoning you for any good work,” they replied, “but for blasphemy, because you, a mere man, claim to be God.”
   34 Jesus answered them, “Is it not written in your Law, ‘I have said you are “gods”’? 35 If he called them ‘gods,’ to whom the word of God came—and Scripture cannot be set aside— 36 what about the one whom the Father set apart as his very own and sent into the world? Why then do you accuse me of blasphemy because I said, ‘I am God’s Son’?

Emphasis mine, of course. The part in bold made me think that these were prophets, but let's check the reference to be sure.

  Psalm 82  (NIV)
  A psalm of Asaph.
   1 God presides in the great assembly;
     he renders judgment among the “gods”:
   2 “How long will you defend the unjust
     and show partiality to the wicked?
  3 Defend the weak and the fatherless;
     uphold the cause of the poor and the oppressed.
  4 Rescue the weak and the needy;
     deliver them from the hand of the wicked.
   5 “The ‘gods’ know nothing, they understand nothing.
     They walk about in darkness;
     all the foundations of the earth are shaken.
   6 “I said, ‘You are “gods”;
     you are all sons of the Most High.’
  7 But you will die like mere mortals;
     you will fall like every other ruler.”
   8 Rise up, O God, judge the earth,
     for all the nations are your inheritance.

Huh, this passage seems to be talking about judges, not prophets. However, remember that in ancient Israel, judges and prophets were often the same people1.

Now the question becomes: why call these people "gods"? One readily apparent reason is that God is the great Judge, hence these judges are gods in that sense. Another, less clear and more speculative reason, has to do with them being prophets. Taking parts of two verses and putting them near each other...

  John 10:35b - to whom the word of God came

  Psalm 82:6b - you are all sons of the Most High

...it would seem like they are related by God's Spirit somehow. An analogue can be found in the New Testament with regards to Christians being brothers and sisters in Christ.

  Hebrews 2:11 (NIV)
  11 Both the one who makes people holy and those who are made holy are of the same family. So Jesus is not ashamed to call them brothers and sisters.

  Romans 8:29 (NIV)
  29 For those God foreknew he also predestined to be conformed to the image of his Son, that he might be the firstborn among many brothers and sisters.

Similarly, God's prophets could be called "gods" due to their association with the Holy Spirit.

1 If someone could point me to a source for this, I'd greatly appreciate it.


What is the Catholic position on ethnic parishes today?

My church (Roman Catholic, on the south coast of the UK) hosts a monthly Mass in Polish, which is well attended. The building was packed for the Polish "Midnight" Mass at Christmas.

It also hosts a weekly (Sunday afternoon) Mass for the Ordinariate congregation, whose members are not members of the local diocese.

In all these efforts, including the Hispanic Masses you reference, I would like to think that the Church is not just seeking to get people in the door, but providing a ministry. It is to be hoped that immigrant churchgoers will seek to assimilate themselves into the local culture, and there is at least a weekly opportunity to attend Mass in English, which would fulfil an obligation. But such assimilation may take some considerable time. If the Church can provide the opportunity for confession and Mass in a native language, and allow full participation in the rites of Church, then why not?

[The answer to Why not is, of course, your point about making fully-fledged parishioners. However in our case, it's quite likely that members of the Polish community are not long-term residents. We do have a sizable Italian Catholic community, and they do attend Masses in English.]


The bee represents Mary, the mother of Jesus. (In fact, it's a fairly safe bet that just about anything represents Jesus or Mary or both.) Other versions of the Exultet text make this explicit; the "Franco-Roman version" has a long we-love-bees section, as recorded by Thomas Forrest Kelley in his The Exultet in Southern Italy (OUP, 1996), p38, concluding with:

O vere mirabilis apis cuius nec sexum masculi violant, fetus non quassat nec filii destruunt castitatem. Sicut sancta concepit virgo Maria, virgo peperit et virgo permansit.
O truly marvelous bee, whose sex is not violated by the male, nor shattered by childbearing, neither do children destroy her chastity. Just as holy Mary conceived as a virgin, gave birth as a virgin, and remained a virgin.

This alludes to the old belief that bees reproduced asexually. Isidore reports in Etymologiae 12.8 that bees, like other small flying animals, are spontaneously generated from the carcasses of animals. So also, Augustine says in City of God 15.27 that bees have no distinction of male and female (alia vero in quibus nihil sit maris et feminae, sicut apes). This comes from ancient sources: Pliny in Natural History 11.16 suggests that they might weave their young out of parts of flowers; and Aristotle (On the generation of animals 2.10) says they are hermaphrodites, and do not copulate with one another.
We now know that they really couldn't have been more wrong, but the sentiment is there.
We have several copies of "Exultet rolls" which have bee illustrations to accompany the vigil text, indicating the great interest and respect that people had for them. Here is an eleventh century one, from Bari (Archivio del Capitolo Metropolitano, Exultet 1).

Bees were an example of industry, and esteemed because they provided so many useful things - in particular, honey and light (via the candle). Both honey and light have obvious Biblical resonances. Additionally, gifted orators and writers were said to have a "honeyed tongue", and so some saints may be depicted with accompanying bees (e.g. Ambrose, Anthony of Padua, Bernard of Clairvaux, Isidore of Seville).


What do Evangelical Protestants mean by "receive Jesus"?

For Evangelicals, "receiving Jesus" can be considered to be functionally equivalent to one or more of the following:

Regeneration
Being born again
Receiving the (indwelling) Holy Spirit
Being justified by faith
Being adopted into the family of God
Being saved
Conversion
Making a decision
Praying through

Evangelicalism is somewhat of a moveable feast and different Evangelicals will have their own favoured terminology - sometimes treating the other terms listed here as synonyms, and sometimes emphasizing distinctions between them.

This doctrine stands at the core of Evangelicalism, and as such there are many more scriptural passages that have been cited in support of it than is appropriate to reproduce here. Nevertheless, here are ten passages that are very commonly linked with it:

Ezekiel 36:26-27

  I will give you a new heart and put a new spirit in you; I will remove from you your heart of stone and give you a heart of flesh. And I will put my Spirit in you and move you to follow my decrees and be careful to keep my laws.

John 3:3

  Jesus replied, “Very truly I tell you, no one can see the kingdom of God unless they are born again.

John 14:16-17

  And I will ask the Father, and he will give you another advocate to help you and be with you forever— the Spirit of truth. The world cannot accept him, because it neither sees him nor knows him. But you know him, for he lives with you and will be in you.

Romans 5:1-2

  Therefore, since we have been justified through faith, we have peace with God through our Lord Jesus Christ, through whom we have gained access by faith into this grace in which we now stand. And we boast in the hope of the glory of God.

Romans 8:8-10

  Those who are in the realm of the flesh cannot please God. You, however, are not in the realm of the flesh but are in the realm of the Spirit, if indeed the Spirit of God lives in you. And if anyone does not have the Spirit of Christ, they do not belong to Christ. But if Christ is in you, then even though your body is subject to death because of sin, the Spirit gives life because of righteousness.

Romans 8:14-16

  For those who are led by the Spirit of God are the children of God. The Spirit you received does not make you slaves, so that you live in fear again; rather, the Spirit you received brought about your adoption to sonship. And by him we cry, “Abba, Father.” The Spirit himself testifies with our spirit that we are God’s children.

Romans 10:9-10

  If you declare with your mouth, “Jesus is Lord,” and believe in your heart that God raised him from the dead, you will be saved. For it is with your heart that you believe and are justified, and it is with your mouth that you profess your faith and are saved.

2 Corinthians 5:17

  Therefore, if anyone is in Christ, the new creation has come: The old has gone, the new is here!

Colossians 1:26-27

  the mystery that has been kept hidden for ages and generations, but is now disclosed to the Lord’s people. To them God has chosen to make known among the Gentiles the glorious riches of this mystery, which is Christ in you, the hope of glory.

Revelation 3:20

  Here I am! I stand at the door and knock. If anyone hears my voice and opens the door, I will come in and eat with that person, and they with me.


When did the practice of tearing one's own garments start among the Jews?

Genesis 37:29 (NIV):

  29 When Reuben returned to the cistern and saw that Joseph was not
  there, he tore his clothes.

This is the earliest mention I can find among the descendants of Abraham. Reuben, son of Jacob was distraught that his nine brothers had sold their other brother Joseph into slavery.

In Job, we see both Job and his three friends doing this:

  Job 1:20 At this, Job got up and tore his robe and shaved his head.
  Then he fell to the ground in worship.

  Job 2:12 When they saw him from a distance, they could hardly
  recognize him; they began to weep aloud, and they tore their robes and
  sprinkled dust on their heads.

In this case, it was to display mourning and sympathy.

There is little agreement over when Job lived, but my best understanding is that he lived between Abraham and Moses. Thus this practice would seem to be common in the Ancient Near East, not just among Jews, but also among the neighboring peoples.


What is the "paradise" that Jesus references in Luke 23:43?

While this isn't a universal view, many traditions believe that Paradise is distinct from Heaven. Our Church (a Baptist Church) teaches that "Paradise" is a temporary holding place for those who have died and are awaiting Christ's return.

Some other references that point to Paradise being a temporary place, distinct from the final Heaven promised to those who have been saved:

http://www.bible-uk.com/paradise.htm

  So what IS Paradise?

  The concept of a place of limbo, somewhere between heaven and earth,
  some kind of celestial waiting room is not one that will be found in
  the pages of scripture. What about a park or garden? Now we are on a
  firm biblical path! We know of a garden from the early pages of
  Genesis, called the Garden of Eden. We know, because Adam and Eve were
  thrust out of it (Genesis 3:24) and were unable to get back in again,
  which fits well with original Persian concept of Paradise being an
  enclosed garden. Equating Paradise with Eden is not something new or
  unusual. It is the rationale behind Milton's book, "Paradise Lost",
  for instance.

Also:

http://www.christianitytoday.com/ct/2003/november/24.79.html

http://www.wor.org/Books/p/Paraking.htm

There are many more, so I'll stop here. I'd also like to post a disclaimer that I don't agree with all of the things said in the last article linked to. It was included just to show that diverse traditions hold the view, and that it's not a "fringe" view.


How many people were killed by the Sanhedrin around the time of Paul?

How many they killed is not easy to know in absence of any historical records. They must have killed many and they did conspire to kill these three prominent ones and few more.The Sanhedrin did not have the power under Roman authority to put someone to death (Jn 18:31). This power was supposedly revoked in 30 A.D. But that did not keep them from hatching conspiracies in these meetings to get their opponets killed and they were only short of passing a formal death sentence.

Plotted to kill Jesus through Romans:

In absence of this power, Sanhedrin plotted to have Him murdered (Jn 11:47-53), paid Judas Iscariot 30 pieces of silver to betray Jesus (Mt 26:14-16)(Mk 14:10-11)(Lk 22:1-6), had Him arrested and tried Him using false witnesses to accuse Him (Mt 26:47-66)(Mk 14:43-65)(Lk 22:47-53)(Jn 18:1-27), then pressured Pontus Pilate into having Him crucified (Mt 27:1-26)(Mk 15:1-15)(Lk 23:1-25)(Jn 18:28-19:16).

Also  this court was to meet every day during daytime hours and was not to meet on the Sabbath or holy days,but broke this rule to condemn Jesus.

They plotted to kill James the just and Stephan:

According to the Jewish historian Josephus, in 62 A.D. the High Priest named Ananus assembled a Sanhedrin who condemned James, the Lord's brother, "on the charge of breaking the law" and had him stoned to death.

They also got Stephan killed by infuriating a mob:The Sanhedrin listened to the charges brought against Stephen (Acts 6:8-7:1) and then allowed the murder of Stephen by stoning (Acts 7:54-60).

Also in addition to these three:

The Sanhedrin also ordered Peter and John not to proclaim the name of Jesus (Acts 4:1-22), and when they would not stop, they had them beaten (Acts 5:17-42).

Paul was brought before the Sanhedrin and spoke to them (Acts 22:30-23:6), and afterwards they conspired to murder him (Acts 23:12-22).

Why this historical nuance?

Truly the Stakes were  very high and if we agree with your view that "Sanhedrin that condemn one man to death in 75 years is bloody" then killing of these prominent three, can be only described as a knee jerk action in a do or die situation to arrest a budding movement that was to change the face of this world. Jewish authorities had rightly judged this movement as not any ordinary one.  Jews had already lost their political clout and now they were in the process of  losing their religious hold on general Jewish public. This echoed in Bible:

John 11:47–48

  Then gathered the chief priests and the Pharisees a council, and said, What do we? for this man doeth many miracles. If we let him thus alone, all men will believe on him: and the Romans shall come and take away both our place and nation.


How could Abraham have possibly dined physically with God as suggested
  in Genesis 18, especially when "No one has ever seen Him"?

My understanding something like this (my own Trinitarian version).

Before incarnation, all the 3 person of Trinity has one name which is in that time the name is called Yahweh.

After incarnation, all the 3 person of Trinity has one name which is in that time the name is called Jesus.

The First Person will never be seen by human because the world won't be able to contain it, while The Second Person is every event when human see Him in a "limited" state.

1 Timothy 6:16 and John 6:46 is speaking about Jesus the Father (First Person)

Genesis 18:1-8 (and maybe some other verses) is speaking about Yahweh the Son (Second Person).

I'm not sure though :).


Are people possessed by demons today? What is the modern Christian perspective?

Yes, people can be possessed by demons today. There is no particular Scripture to indicate that anything changed form the time that Jesus pronounced certain people as possessed to now.

It's very important to remember that Jesus is always trump. The disciples were amazed to find that even the spirit world (however that manifest itself) was subject to the the authority of Christ and his teachings1, not just when he gave them but when they went out to proclaim them2.

Also, it's not something focus on or draw our attention from the main message of the Gospel3. It's sort of an incidental problem that we overcome just like any other problem in this world. Undue focus on the realms of evil, spirit or physical, is unhealthy. In fact many things are often mistaken for spirit world problems that are just the fruits of our flesh. Sorcery is one example4.

Lastly, Christians cannot be possessed. The enemy has no authority over the temple of the Holy Spirit. Christians have been raised into life with Christ and are temples of the Holy Spirit. Those temples are are off limits to the enemy because the victory has already been won5 and we have been transferred from the kingdom of darkness to that of light6.

Mark 1:27 (ESV)
And they were all amazed, so that they questioned among themselves, saying, “What is this? A new teaching with authority! He commands even the unclean spirits, and they obey him.”
Luke 10:17-19 (ESV)
The seventy-two returned with joy, saying, “Lord, even the demons are subject to us in your name!” And he said to them, “I saw Satan fall like lightning from heaven. Behold, I have given you authority to tread on serpents and scorpions, and over all the power of the enemy, and nothing shall hurt you.
Luke 10:17-20 (ESV)
Nevertheless, do not rejoice in this, that the spirits are subject to you, but rejoice that your names are written in heaven.”
Galatians 5:19-21 (ESV)
Now the works of the flesh are evident: sexual immorality, impurity, sensuality, idolatry, sorcery, enmity, strife, jealousy, fits of anger, rivalries, dissensions, divisions, envy, drunkenness, orgies, and things like these. I warn you, as I warned you before, that those who do such things will not inherit the kingdom of God.
Colossians 2:15 (ESV)
He disarmed the rulers and authorities and put them to open shame, by triumphing over them in him.
Colossians 1:13 (ESV)
He has delivered us from the domain of darkness and transferred us to the kingdom of his beloved Son


According to Catholicism, how many heavens are there?

The book of Enoch is not part of the canon of the Jewish Tanakh nor the Christian/Catholic Bible. Meaning that it is not accepted as authoritative by jewish or christians. This book is used as part of the kabbalistic literature in the zohar, that in itself could tell you that it is not a great source of information to use for knowing about God (it can be used for knowing a god, satan).
There are three heavens named in the Bible (Deut 10:14), the first is the sky where there are clouds and birds (Gen 1:8, 20; Deut 11:17; Judg 5:4), the second is the space where are planets and stars (Gen 15:5; Psa 19:4-6; Deut 17:3), and the third is the methapysical heaven (Matt 6:9; 2 Cor 12:2; Eph 4:10) where Jesus Christ went.


This one line "Where there is a dead body, there the vultures will gather." is parable.
This would be the equivalent of saying, "Where there's smoke, there's fire."

Long answer:
Where, Lord?
The question that Jesus is responding to is also a bit confusing (particularly given our modern understanding of the rapture).  However, the question of "Where, Lord?" seems to be addressing the last thing Jesus says.  He just finished saying that the "Son of Man" will come and gather his people.  The disciples' question seems to ask "Where will they be gathered to."
This very much is a reference to what we call the "rapture".  This is the "gathering up" of people that Jesus will perform in the last days.  Just before this he talks about how the world is turning evil and then he says that he will come back and gather his people.  This is definitely what we modernly call the "rapture".
Jesus replies
His reply to the question of "Where, Lord?" is a parable.  He's basically saying, "Where there's smoke, there's fire."  The meaning behind this is:
"That should be pretty obvious to you."
Jesus was saying that his kingdom was coming, the world was about to end, he was about to gather his people.  The disciples ask a stupid question: "Where will you gather them?"  Jesus doesn't even bother giving a straight answer because the answer is obvious:  He's gathering them to heaven to be with him forever.
Why use a parable?
The reason that the answer is obvious is because, he's already answered that question.  Just previously in Luke 17:20-21 the passage begins Jesus' speech with "The coming of the kingdom of God is not something that can be observed."
The entire speech is about the Kingdom of God.  So when they ask, "Where will they be gathered."  He just replies in parables, since he's already made it obvious.
Summary
This phrase about vultures and a dead body is just Jesus way of saying, "Hey, it should be obvious".  He's not trying to imply anything with vultures or dead bodies.  Just like the phrase "Where there's smoke there's fire" today does not imply smoke, fire, or anything related to smoke or fire.


Has there been a shift in Christian metaphysics from a unitary cosmos to a binary one?

It seems to me that before the Enlightenment, the predominant
  understanding of the structure of the universe was that the cosmos,
  while stratified, is unitary- that "the Heavens", which include the
  spheres of the stars, then of the angels, and the abode of YHWH, have
  substantial existence in the same way that the Earth does.

When one speaks of Christian beliefs, one must recall that the beliefs which developed in the west - particularly in the medieval period, perhaps beginning with Charlemagne - were in some cases radically different from the beliefs held by the eastern Christians that now, for the most part, form the Orthodox Church.

I don't think any of the Church Fathers had a belief that the abode of God and His angels had any kind of "substantial" existence.

John of Damascus (8th century) explained:

  The heaven [sic] is the circumference of things created, both visible
  and invisible.  For within its boundary are included and marked off
  both the mental faculties of angels and all the world of sense.  But
  the Deity alone is uncircumscribed, filling all things, and
  surrounding all things, and hounding all things, for He is above all
  things, and has created all things.  For the great part the
  heaven is greater than the earth, but we need not investigate the
  essence of heaven, for it is quite beyond our knowledge.
  -- An Exact Exposition of the Orthodox Faith, Book III


What is the source of hatred often perceived by Christians in western society?

I don't think that Christians face any more bigotry than any other group.  As TRiG pointed out in his answer, there are many American Christians who have chosen to interpret their loss of special privilege in our culture to be "hatred against Christians", when in reality it results not from hatred, but from a desire for equality.

However, there are those who fear Christians, and fear is easy to mistake for hatred. There was a time when I just didn't get the fear that some people showed toward Christians.  Then the military stationed my family in the Bible Belt...

A Christian neighbor found out that my family is not Christian.  She called a local Christian preacher, who tried to break into my house with the stated goal of beating me until I miscarried (I was 6.5 months pregnant).  The (apparently Christian) police refused to come to my aid.
My (Jewish) friend's child innocently and accidentally outed himself to his Christian first grade classmates; they beat him so badly he spent three days in intensive care.
My Catholic mother was harassed and kicked out of a quilt shop for not being the "right" kind of Christian.
I spent time with a Red Cross worker who had come from trying to restore the economies in third-world communities where Christian missionaries had disrupted the food supply, local medical care, and more in their attempts to convert the locals.
I watched Christian babies in the NICU denied the breast milk that could have bolstered their immune systems because the local Christian sects taught that breastfeeding was a sin.
I saw a Christian chaplain deny needed services to people who put their lives on the line for our country, because he did not believe that non-Christians were deserving of his time.

Because much of my extended family is Christian, I have exposure to Christians who aren't violent, destructive, sex offenders, or trying to force their religion on others through economic and/or political coercion.  The thing is, most non-Christians only run into Christians when they are doing these things, so they believe that such behavior is emblematic of mainstream Christianity.  To my knowledge, of these practices only missionary work is mainstream -- and the destruction caused is usually not intentional, but the result of ignorance about social and economic systems they are affecting.

Unfortunately, most Christians seem to think that if they quietly ignore these problems, they will go away.  However, until the sane Christians publicly step in when the fringe gets out of control, the fringe will continue to be all that non-Christians see, and they'll have defined Christianity for most outsiders.


Prior to Cyrus the Great, a Persian, the Medians were overlords of the Persians and other tribes in what is now western Iran.  Cyrus overthrew the Median king, Astyages, and founded the Achaemenid Empire, with the Media as part of the empire.  Cyrus went on to conquer Babylon in 540 BCE and soon after allowed the Jews to return to Jerusalem, for which he is mentioned extensively in 2 Chronicles, Ezra and Isaiah (Second Isaiah) by the grateful Jews.

Cyrus was killed in battle in about 530 BCE, in Central Asia, and was succeeded by his son, Cambyses. In 522 BCE, while Cambyses was campaigning in the west, a usurper, Bardia or Smerdis, occupied the throne. He was quickly overthrown by Darius, who, although a Mede, was a military commander in the Persian empire. Darius I ruled Persia from 522 until 486 BCE and was succeeded by his son Xerxes (known as 'Ahasuerus' in the Bible).

The Cambridge Ancient History Volume III Part 2, page 395, says the Book of Daniel is generally considered to be a historically unreliable compilation of the second century BCE. Two of the historical errors in the Book of Daniel were to describe to Darius "the Mede" as the son of Xerxes and as the king who conquered Babylon, at the age of sixty two (18 years before he overthrew Smerdis and really became king):

  Daniel 5:31: And Darius the Median took the kingdom, being about threescore and two years old.

An alternative view

Sara Raup Johnson (Historical Fictions and Hellenistic Jewish Identity, page 58) provides the background to another interesting explanation of "Darius the Mede". She tells us that Josephus, writing late in the first century CE, was baffled by the reference to "Darius the Mede", who ruled before Cyrus according to the Book of Daniel. Jewish Antiquities Book 10 closely follows the Book of Daniel, but Josephus is unable to identify another historical Darius who would preserve Daniel as a book of history. Johnson says that Josephus came up with a characteristically ingenious solution. Josephus wrote that Darius the Mede was a son of Astyarges the Mede, maternal grandfather of Cyrus "but was called another name among the Greeks", and that he assisted Cyrus in the overthrow of Babylon. She says (Page 59) that Josephus stands at the head of a line leading to modern scholarship's vain attempts to make historical sense of texts never written as pure history.

Steven Anderson (https://www.academia.edu/9787699/Darius_the_Mede_A_Reappraisal) looks at some options for 'Darius the Mede' to have taken part in the conquest of Babylon. A critical assumption in this dissertation is that 'Darius the Mede' either existed or he did not; Anderson does not consider the possibility that Daniel's author displaced King Darius I in time.   At page 51, he acknowledges that mainstream scholarship says that the Book of Daniel was a compilation of the second century BCE, at the same time cautiously raising his own doubts on this. The problem is that if the Book of Daniel was a late, pseudepigraphical work, we have no reason to believe it to be historically accurate. Anderson acknowledges that Jerome cited Josephus, whom Anderson acknowledges (page 5) as appearing to have been the first  to identify Daniel’s Darius the Mede with Xenophon’s Cyaxares II. Thus, Josephus was the only independent source for this claim, and he is already well known for taking a biased view of history when it suited.


Where are the manuscripts of Dean John Burgon?

Worldcat is an excellent resource for locating rare books in libraries. Once you select a title, it lists different libraries that have it in their collections.

This search shows all works of Dean John William Burgon in any library. There isn’t a way to search by location, so you may need to look through a good number of them to find which specific titles are nearby. You may also need to do some digging and see if you can request the book from a library that’s a bit farther off.


What soteriological doctrines are most prevalent within Protestantism throughout the world?

Below I have reproduced a table from a 2011 Pew study on Christian Movements and Denominations which used data from the Gordon-Conwell Theological Seminary Center for the Study of Global Christianity.

+-----------------------------------------------------+-------------------------------+
|                Denominational family                | Percentage of all Protestants |
+-----------------------------------------------------+-------------------------------+
| Historically pentecostal denomination               | 10.8%                         |
| Anglican                                            | 10.6%                         |
| Lutheran                                            | 9.7%                          |
| Baptist                                             | 9.0%                          |
| United churches (unions of different denominations) | 7.2%                          |
| Presbyterian or Reformed                            | 7.0%                          |
| Methodist                                           | 3.4%                          |
| Adventist                                           | 2.7%                          |
| Congregationalist                                   | 0.5%                          |
| Brethren                                            | 0.5%                          |
| Salvation Army                                      | 0.3%                          |
| Moravian                                            | 0.1%                          |
| Other (independent, nondenominational and others)   | 38.2%                         |
+-----------------------------------------------------+-------------------------------+

I would classify each of these denominations as one of the following:

Lutheran: influenced by the theology of Martin Luther, the father of the Reformation. Over time, Lutheranism has evolved on the issue of soteriology, but it remains distinct from Calvinism and Arminianism while emphasizing the principle of sola fide (salvation by faith alone), which is common to all Protestant denominations. Above, Lutherans (obviously) and Moravians would qualify as Lutheran.
Arminian: influenced by the theology of Jacob Arminius, whose followers drafted the Five Articles of Remonstrance in opposition to what they perceived as errors in Reformed soteriology. Arminian denominations also have a historical connection to the teachings of John Wesley, an avowed Arminian. Above, these denominations include Pentecostalism, Methodism, Adventism, and the Salvation Army.
Reformed: influenced by the theology of John Calvin, and united in adherence to the five points of Calvinism, which are summarized in the acronym TULIP and based on articles drafted at the Synod of Dort in response to the Five Articles of Remonstrance. Above, I would only classify "Presbyterian or Reformed" as Reformed.
Anabaptist: rooted in the Radical Reformation, which occurred at the same time as the Reformation but took a different tack. Early Anabaptists have been called proto-Arminians, and among modern Anabaptists you'll be hard-pressed to find any Calvinists; you'll either find people close to Arminianism, or adherents of open theism, which is even further from Calvinist doctrine. Above, I would only classify "Brethren" churches as Anabaptist.
Mixed: many denominations have no stance on these soteriological doctrines. While individuals (or individual congregations, or even the odd denominational institution) may have their own convictions, the Anglican, Baptist, United, and Congregationalist families as a whole do not take a position on Calvinism or Arminianism.

Another complication is that individuals may or may not adhere to the official or traditional teachings of their denomination. For example, though Pentecostalism is rooted in the Wesleyan/Holiness movement, as of 2010 31% of American Pentecostal/charismatic pastors described themselves as reformed according to Barna Research.

But below, I have used the original Pew table to demonstrate what percentage of world Protestants belong to denominational families that are either Lutheran, Reformed, Anabaptist, or mixed.

+---------------------------------------------+-------------------------------+
| Denominational family's soteriological bent | Percentage of all Protestants |
+---------------------------------------------+-------------------------------+
| Mixed                                       | 65.5%                         |
| Arminian                                    | 17.2%                         |
| Lutheran                                    | 9.8%                          |
| Reformed                                    | 7.0%                          |
| Anabaptist                                  | 0.5%                          |
+---------------------------------------------+-------------------------------+

I haven't been able to find good statistics on how many Protestants in the "mixed" category identify as Calvinists, how many identify as Arminians, and how many would identify as some kind of "other." Affable Geek has a couple posts on this site explaining how a lot of Baptists let Calvinist and Arminian principles operate side-by-side.


What formal methods and criteria could be used to evaluate the message of the bible?

I used to be in the same position as your friend, and it took me many years to take the claims of the Bible seriously.
At the time, I was doing a degree in Philosophy of Science, which discusses the nature of scientific evidence. One of the key principles is the Duhem-Quine Thesis, which states that it is impossible to test a hypothesis in isolation. That is, you cannot directly test the truth, only the effects of the truth.
As I began to explore the Bible, I found I engaged with it in a similar way. The Bible presents a certain world view, and I needed to ask myself whether the effects of that world view was what I saw around me.
In light of this, I would say the writers of the Bible put forward three pieces of evidence for the truth of the gospel (or, at least, these are the three that helped me).
Historical eye-witness of the ressurection
The Apostle Paul spends the first half of 1 Corinthians 15 providing the historic, eye-witness evidence for the ressurection:

For what I received I passed on to you as of first importance: that Christ died for our sins according to the Scriptures, that he was buried, that he was raised on the third day according to the Scriptures, and that he appeared to Cephas, and then to the Twelve. After that, he appeared to more than five hundred of the brothers and sisters at the same time, most of whom are still living, though some have fallen asleep. Then he appeared to James, then to all the apostles, and last of all he appeared to me also, as to one abnormally born. 1 Cortinthians 15:3-8 (NIV)

And at the end of his discussion, stresses the absolute importance of this evidence:

And if Christ has not been raised, your faith is futile; you are still in your sins. 1 Corinthians 15:17 (NIV)

The Apostle John also places great weight on eye-witness testimony:

Jesus performed many other signs in the presence of his disciples, which are not recorded in this book. But these are written that you may believe that Jesus is the Messiah, the Son of God, and that by believing you may have life in his name. John 20:30-31 (NIV)

As does Luke:

With this in mind, since I myself have carefully investigated everything from the beginning, I too decided to write an orderly account for you, most excellent Theophilus, so that you may know the certainty of the things you have been taught. Luke 1:3-4 (NIV)

Jesus also teaches this point in Matthew 16, when the Pharisees demand evidence beyond what has already been given:

The Pharisees and Sadducees came to Jesus and tested him by asking him to show them a sign from heaven. He replied, “When evening comes, you say, ‘It will be fair weather, for the sky is red,’ and in the morning, ‘Today it will be stormy, for the sky is red and overcast.’ You know how to interpret the appearance of the sky, but you cannot interpret the signs of the times Matthew 16:1-3 (NIV)

Jesus discusses this incident with his disciples a moment later:

Do you still not understand? Don’t you remember the five loaves for the five thousand, and how many basketfuls you gathered? Or the seven loaves for the four thousand, and how many basketfuls you gathered? Matthew 16:9-10 (NIV)

My understanding of this incident is that Jesus is saying the miracles he has already performed, and have been witnessed by large crowds, are enough evidence. The Pharisees shouldn't need to demand more.
Creation
The Apostle Pauls says that

For since the creation of the world God’s invisible qualities—his eternal power and divine nature—have been clearly seen, being understood from what has been made, so that people are without excuse. Romans 1:20 (NIV)

Creation itself ought to speak on God's behalf. This is both physical nature, like beautiful sunrises and incredible music, since it was made by God. But it also include human nature, like our compassion and sense of justice, since we were made in God's image.
Personally, I would add our observation of suffering and sin into this - and this topic was actually the things that brought me to Jesus. The Bible explains the negative parts of human nature as well as the positive parts, and I believe it explains it far better than any other source I've found. The way in which humans are in constant tension between incredible good and incredible evil can only be adequately explained by the Bible. I found Paul's description of himself very compelling:

I do not understand what I do. For what I want to do I do not do, but what I hate I do...For I have the desire to do what is good, but I cannot carry it out. For I do not do the good I want to do, but the evil I do not want to do—this I keep on doing...So I find this law at work: Although I want to do good, evil is right there with me. Romans 7:15,18,19,21 (NIV)

The Church
The Apostles barely every stop talking about how the church itself is one the primary pieces of evidence for the truth of the gospel:

If I am delayed, you will know how people ought to conduct themselves in God’s household, which is the church of the living God, the pillar and foundation of the truth 1 Timothy 15 (NIV)
Watch your life and doctrine closely. Persevere in them, because if you do, you will save both yourself and your hearers. 1 Timothy 4:16 (NIV)
In everything set them an example by doing what is good. In your teaching show integrity, seriousness and soundness of speech that cannot be condemned, so that those who oppose you may be ashamed because they have nothing bad to say about us. Titus 2:6-8 (NIV)
...so that in every way they will make the teaching about God our Savior attractive. Titus 2:10 (NIV)
Live such good lives among the pagans that, though they accuse you of doing wrong, they may see your good deeds and glorify God on the day he visits us. 1 Peter 2:12 (NIV)

There should be something about the way the church treats people, both inside and outside the church, that shows people the Bible's teaching is true.
Of course, as other have pointed out, ultimately this isn't a logical decision, but a spiritual one. We must pray that God chooses to open the eye's of your friend, as he graciously did for me.


What's so bad about monoergism and monothelitism?

I was trying to explain these two Christological concepts to an unsaved friend of mine, and he said, "Oh, so you're talking about the opposite of demon-possession - that Jesus the man was simply possessed by God."

Stripping that analogy down to its essentials, I think he may be on to something.  If Jesus only had one "energy" or one will, then Jesus is essentially a docetist God, only appearing to be man.  If his humanity is scooped out and overridden by God's indwelling, then he can't really identify with humanity.  To hold to a monothelitist idea is to say that God only "appeared" to be human - but a lobotomized human isn't really all that human.

As such, to hold to this heresy would be to make a mockery of the incarnation.  God may have taken on flesh and bone, but not mind and spirit.

And, if he didn't, then he didn't know jack about every Tom. Dick, and Harry out there...


How many Christian denominations are there?

I'll restate the comment that this is a hard question to answer because it depends on the definition of denomination and it's hard to count/find every single denomination in the world.

The number you state (30,000+) probably comes from The World Christian Encyclopedia, specifically 2nd edition published in 2001. They use the following definition:

  A denomination is defined in this Encyclopedia as an organized aggregate of worship centers or congregations of similar ecclesiastical tradition within a specific country; i.e. as an organized Christian church or tradition or religious group or community of believers, within a specific country, whose component congregations and members are called by the same denominational name in different areas, regarding themselves as one autonomous Christian church distinct from other denominations, churches and traditions. As defined here, world Christianity consists of 6 major ecclesiastico-cultural blocs, divided into 300 major ecclesiastical traditions, composed of over 33,000 distinct denominations in 238 countries, these denominations themselves being composed of over 3,400,000 worship centers, churches or congregations.”1

The Center for the Study of Global Christianity also has statistics that align closely to this number (see #41 in the link-34,200 denominations in 2000).

On a Christianity Statistics article, updated March 2017, states that there are approximately 41,000 Christian denominations, but they also state:

  This statistic takes into consideration cultural distinctions of denominations in different countries, so there is overlapping of many denominations.

The World Christian Database represents over 9,000 Christian denominations. This number is quite lower than 30,000 but it also doesn't say what who exactly is represented or who isn't.

On Wikipedia they list about 1,100 denominations (according to my count) but Wikipedia isn't official.

For more details on the breakdown of (30,000+) read this article (not a primary source).

Based on the statistics from the above article (last link above) and the Christianity Statistics article I graphed the recorded denominations by year and the projected number of denominations in 2025.

All emphasis is added by me

1 https://books.google.com/books?id=FzAJe58A68oC&pg=PA555&lpg=PA555&dq=Barrett+et+al,+volume+1,+page+16,+Table+1-5,&source=bl&ots=WEIH1qILRr&sig=xE2094fUeTzL1MG_KgeA0gq0ZVA&hl=en&sa=X&ved=0ahUKEwiHrZPa-vbSAhWIeCYKHRFLArEQ6AEIKzAC#v=onepage&q=Barrett%20et%20al%2C%20volume%201%2C%20page%2016%2C%20Table%201-5%2C&f=false


Does the Catholic Church prohibit marriage between a woman and her God-father?

Marriage between baptized and sponsor was prohibited in the Latin Church till 1983 and is prohibited in the Eastern Catholic Churches.

Latin Church

The CIC 1917 (Codex iuris canonici, code of canon law) states for the Latin Chuch:

  Can. 768. Ex baptismo spiritualem cognationem contrahunt tantum cum baptizato baptizans et patrinus.

  Can. 797. Etiam ex valida confirmatione oritur inter confirmatum et patrinum cognatio spiritualis, ex qua patrinus obligatione tenetur confirmatum perpetuo sibi commendatum habendi eiusque christianam educationem curandi.

  Can. 1079. Ea tantum spiritualis cognatio matrimonium irritat, de qua in can. 768.

Translation (can. 768 from Eward N. Peters; cann. 798 and 1079 my own, more free):

  can. 768 From baptism a spiritual relationship is contracted only between the baptizing, the one baptized, and the sponsor.

  can. 798 Also from a valid confirmation comes a spiritual relationship between the confirmed et the sponsor, from wich the obligation of the sponsor stays to hold ever a good relationship to the confirmed and to take care of his christian education.

  can. 1079 The spiritual relationship [maybe better: kinship] disturbs only the marriage of the ones named in can. 768.

Can. 1079 is in the chapter about diriment impediments, so a marriage against this canon is void. I intepret it as forbidding only the marriage of baptismal sponsor and baptized, not the marriage of confirmational sponsor and confirmed, but I am not totally sure. This impidiment is seen as of "minor grade" (can. 1042 § 2 n. 4) and can be dispensed from by the Apostolic See (but no other, can. 1040).

This rules were derogated in 1983 when the CIC 1983 came into force. The new code does not know spiritual kinship.

Eastern Catholic Churches

Since 1990 the older canons of the Eastern Catholic Churches are codified into the CCEO (Codex Canonum Ecclesiarum Orientalium, Code of Canons of oriental churches, English here). This code says on this topic:

  Can. 811 - § 1. Ex baptismo oritur inter patrinum et baptizatum eiusque parentes cognatio spiritualis, quae matrimonium dirimit.

  § 2. Si iteratur baptismus sub condicione, cognatio spiritualis non oritur, nisi iterum idem patrinus adhibitus est.

Translation:

  Can. 811 § 1. From baptism there arises a spiritual relationship between a sponsor and the baptized person and the parents of the same that invalidates marriage.

  § 2. If a baptism is repeated under condition, a spiritual relationship does not arise, unless the same sponsor was employed for the second ceremony.

Again from this impediment can be dispensed. This time by the local hierarch (can. 795, bishop/eparch).

Practice

I would expect the dispense in the Eastern Churches to be given without problems, if there is no wrong in the relationship. But they might look closely for hardly imbalanced or even forced relationships. But I have no empirical basis for this claims.

I know of cases in the Latin Church when some married his/her sponsor. This were cases when the two were in a relationship, but only one Christian at the beginning, the other one came to faith (through the partner), got baptized with his/her partner as the sponsor and the two got married nearly afterwards.


During Assyria’s conquest of Israel, what side did Judah take?

In 721 BCE, the Assyrian army captured the Israelite capital at Samaria and carried away the citizens of the northern Kingdom of Israel into captivity. The virtual destruction of Israel left the southern kingdom, Judah, to fend for itself among warring Near-Eastern kingdoms. After the fall of the northern kingdom, the kings of Judah tried to extend their influence and protection to those inhabitants who had not been exiled. They also sought to extend their authority northward into areas previously controlled by the Israeli kingdom.

According to 2 Kings 18, while Sennacherib was besieging Lachish, he received a message from Hezekiah offering to pay tribute in exchange for Assyrian withdrawal. According to the Hebrew Bible, Hezekiah paid 300 talents of silver and 30 talents of gold to Assyria—a price so heavy that he was forced to empty the temple and royal treasury of silver and strip the gold from the doorposts of Solomon's temple. Nevertheless, Sennacherib marched on Jerusalem with a large army. When the Assyrian force arrived, its field commander Rabshakeh brought a message from Sennacherib. In an attempt to demoralize the Judeans, the field commander announced to the people on the city walls that Hezekiah was deceiving them, and that Yahweh could not deliver Jerusalem from the king of Assyria. He listed the gods of other peoples defeated by Sennacherib then asked, "Who of all the gods of these countries has been able to save his land from me?"

During the siege, Hezekiah dressed in sackcloth (a sign of mourning), but the prophet Isaiah assured him that the city would be delivered and Sennacherib would fail.1 Overnight, an angel killed 185,000 Assyrian troops.[2]

All quoted from Wikipedia - Assyrian Siege of Jerusalem


It doesn't and he didn't.

It does say he killed A man. And murder is murder whether you kill one or a thousand,  so he was a murderer.

  Exodus 2:12 (ESV)
  12  He looked this way and that, and seeing no one, he struck down the Egyptian and hid him in the sand.

In my experience, the accusation of 'mass-murder' usually stems from a gross misinterpretation of the Exodus story caused by the presupposition that God was not involved.

If you rule out supernatural intervention, the plague episodes and the Red Sea drownings become folk tales. While nobody expects all the details of such legends to be real, they do assume such tales were based of a 'kernel of truth', and in this case that must have been a temperamental, vindictive and cruel Moses who terrorized the Egyptians in order to achieve his own political ends. It's amazing how twisted a story Exodus becomes if you do not assign God the role he claims for himself in the narrative.


What were people supposed to do with an incomplete or nonexistent Bible?

The entire old testament was available and written before Jesus' time.  The new testament, as we have it is the collected writings of the apostles.  Before all the writings were complete, the apostles taught directly.  After their death, their immediate successors taught what they had learned and during that time the writings were collected, copied and distributed.

Creeds and hymns formed a big part of conveying biblical doctrine before a printed bible was widely available to all, as did the church teaching and structure.  The documents themselves were available to clergy from very early times, soon after the apostolic day.

So at first, there was the testimony of direct witnesses.  Then there was teaching from those taught by the apostles and the apostles written records.  Finally those records were compiled into the bible, and between the mid 300s and late 600s AD the canon of authoritative scripture was considered closed by most traditions, although the Catholic church did not formally declare the bible canons closed until the council of Trent in 1546 with the only disagreement with other traditions being the OT deuterocanonical books (and bear in mind, too, that the Catholic church (and perhaps others), holds to a continued revelation through the church's magisterial office and authority).


Who are the "Sons of Israel" mentioned in Numbers 28

As has been said above, "Sons of Israel" refers to, literally, the 12 sons of the man Israel. However, It also refers to their children, etc. - and thus is another name for the Israelites. (Note that this manner of naming was a common practice - Jos 15:14 for example)

I did not search to determine what translation you are using, but in the KJV and NIV84 the verse definitely seems more clear than that which you are reading from - however, in answer to your question, from the context of the end of chapter 27 of the book, the phrase for children/sons of Israel, does seem to be referring to all of them. There is no indication of anything else occurring, and there is no theological nor practical prevention of this being the case. I understand why you ask the question, as it does seem like rather technical information being passed on here - but there's no reason to think that those to whom it is being spoken are only the levites, priests, or some specific group.

One could certainly speculate as to why God had this spoken to all of Israel, but I think in knowing the purpose of the law and commandments, the purpose of this telling-forth of the required sacrifices is more clear.


Swear to tell the truth 'so help me God'?

My understanding is that the passage quoted does not forbid all oaths in general, but in specific was addressing the practice of the Scribes and Pharisees, who were invoking the name of God, or heaven in their oaths, and breaking them.  I don't see myself where the Scribes or Pharisees are mentioned specifically.

I'd have to study it out further, but I do believe that he was teaching based on a general lack of reverence for the name of God.  Taking an oath made in God's name is serious, which is why Jesus warned us to let our yes be yes and our no be no.  It is better not to swear on the name of God than to swear and break it.

There's an excellent article on this here: http://www.reformed.org/webfiles/antithesis/index.html?mainframe=/webfiles/antithesis/v1n1/ant_v1n1_oaths.html

In it, the author explains how and why this applied to the Scribes and Pharisees, not to all oaths in general.

It goes on to cite scriptures in the bible where we are expected, and even commanded to swear oaths in the name of God in certain occasions.

The following is a small excerpt from the articles, where this is explained, with scripture references:

  The general context of Scripture, when studied carefully, reveals that
  God does not forbid all oaths.

  First, Scripture commands us to swear by the name of God on certain
  occasions. In Deuteronomy 6:13, for example, Scripture commands God's
  people "You shall fear only the Lord your God; and you shall worship
  Him, and swear by His name." Far from prohibiting all oaths, Isaiah
  tells us that "he who swears in the earth shall swear by the name of
  God" (Is. 65:16). God sanctions lawful oaths to such an extent that He
  promises to build up those who swear by His name (Jer. 12:16). Even in
  the mundane affairs of life, such as confirming the truth between
  disputing neighbors, God commands His people to swear before Him (Ex.
  22:10-11). Because Scripture commands God's people to swear by His
  name, it cannot forbid all oaths. God does not command what He
  simultaneously condemns!

  Second, Scripture also teaches us that swearing is an act of
  confession and religious worship. We already saw in Deuteronomy 6:13
  that God commands us to swear in His name precisely because swearing
  in God's name is but one way to worship and fear Him (cf Deut.10:20).
  Isaiah confirms this connection between swearing and worship; when he
  prophesies about the Assyrians and Egyptians coming into a covenantal
  relationship with God, he says that they will swear in the name of
  God. (Is. 19:18). Calvin explains that "by swearing in the Lord's name
  they will profess his religion."[6]

  But exactly how is swearing an act of confession and worship? When we
  duly swear in God's name, we confess several things about God. To
  begin with, we confess that God exists. Moreover, we confess several
  of God's attributes as revealed to us in Scripture: we testify that He
  is omnipresent and omniscient, that He is eternal and immutable, that
  He is just and true, that He is powerful and wrathful. By confessing
  His existence and attributes, we also confess that He is the Supreme
  Judge over all the earth and that we are accountable to Him for all
  that we do and say. Though the word of men may fail, the word of God
  never fails. Though men may fail, God never fails. By taking oaths in
  God's name, we confess God to be the ultimate arbiter of truth, and we
  worship the God of truth in spirit and in truth.

Finally, in the context of swearing in in court, or an oath of office, the practice started when more people understood and respected the gravity of swearing such an oath.  It was meant to be binding.

They believed, correctly, that an oath sworn in God's name should carry more weight, and that it is a serious thing to break it.  Whether or not people still see it that way, or if we're merely repeating words these days, is open to debate, and likely as individual as those taking the oaths.


What is the Catholic Church's historical position on capital punishment: how did we get here?

Wikipedia's article on this topic is a pretty good place to start, and for in-depth treatment, you'll want By Man Shall His Blood Be Shed (Feser and Bessette; in favor of the death penalty) and Capital Punishment and Roman Catholic Moral Tradition (Brugger; against).  Also useful is Laurence's "He Beareth Not the Sword in Vain," a 2003 article on the subject.
To distinguish this answer from these works, I'll focus on summarizing key landmarks in the history of the Church's views on this subject.  I'll rely primarily on Feser, Bessette, and Laurence – unfortunately Brugger's work isn't available to me, but thankfully Feser and Bessette interact with and quote him.
Early church
Church fathers widely accepted the legitimacy of capital punishment, though they varied in their views on how extensively it should be used.  Feser and Bessette view it as a major concession that Brugger, an opponent of the death penalty, is forced to admit:

For the Fathers of the early Church, the authority of the state to kill malefactors is taken for granted. Opinions differed on whether Christians should hold offices whose responsibilities include the judging and carrying out of capital punishments—pre-Constantinian authors said they should not, those writing after AD 313 said they should—but the principled legitimacy of the punishment itself is never questioned (74)

Feser and Bessette cite a number of examples, including Ambrose (Letter 90 / 25, to Studius), Chrysostom (Homilies on the Statues, 6), Augustine (City of God 1.21), and Jerome (Commentary on Jeremiah, Book 4, on 22:3). Also significant is the writing of Pope Innocent I, who refused to condemn Christian civil authorities who carried out the penalty:

About these things we read nothing definitive from the forefathers. For they had remembered that these powers had been granted by God and that for the sake of punishing harmdoers the sword had been allowed; in this way a minister of God, an avenger, has been given. How therefore would they criticize something which they see to have been granted through the authority of God? (Epistle 6, to Exsuperium)

Some opposed the death penalty more intensely, like Tertullian, but even he, say Feser and Bessette, did not oppose it in principle, but rather only that Christians should not participate in it (De Idolatria 19).  (Incidentally, in the same work, Tertullian also taught that Christians should not be school teachers).
Medieval period
In the medieval era, a few landmarks are worth noting.
First, Pope Nicholas I (d. 867) urged civil leaders to avoid using the death penalty, but did not call it illegitimate:

Just as Christ led you back from everlasting death . . . to eternal life, so you yourselves should save not only those who are innocent, but truly also the guilty from the destruction of death. (Epistula XCVII, quoted in Laurence)

Second, major theologians and canonists affirmed the legitimacy of the state exercising capital punishment, including Gratian, Aquinas, and Duns Scotus.  Gratian writes:

It appears therefore that by means of men bearing lawful power . . . wicked men are not only scourged for their sins, but they are also properly put to death. (Decretum, Part II, Cause 23, Question 5)

Aquinas deals with this in his Summa, Book II-II, Question 64, Article 2:

Therefore if a man be dangerous and infectious to the community, on account of some sin, it is praiseworthy and advantageous that he be killed in order to safeguard the common good, since "a little leaven corrupteth the whole lump" (1 Corinthians 5:6).

Third, in the context of the readmission of heretics to the Catholic Church, Pope Innocent III, in 1210, required that former Waldenses affirm that "the secular power can, without mortal sin, exercise judgment of blood."  This is significant, Feser and Bessette argue, because it suggests that acceptance of the death penalty was a necessary component of Catholic orthodoxy.
Reformation era to mid-20th century
The "Roman Catechism" of the Council of Trent addresses this issue in the context of Ten Commandments, and says:

Another kind of lawful slaying belongs to civil authorities, to whom is entrusted power of life and death, by the legal and judicious exercise of which they punish the guilty and protect the innocent.

In the 19th and 20th centuries, popes exercising civil authority did not oppose the practice.  Giovanni Battista Bugatti was the official executioner for the Papal States from 1796 to 1865, and put hundreds to death.  Regarding more recent times, Cardinal Avery Dulles writes:

The Vatican City State from 1929 until 1969 had a penal code that included the death penalty for anyone who might attempt to assassinate the pope ("Catholicism and Capital Punishment")

At least two encyclicals of this period support the legitimacy of the practice, Pastoralis Officii (1891) and Casti Connubii (1930), and Pius XII in several addresses in the 1950s supports it, perhaps most famously saying:

Even when it is a question of the execution of a man condemned to death, the State does not dispose of the individual’s right to live. It is reserved rather to the public authority to deprive the criminal of the benefit of life when already, by his crime, he has deprived himself of the right to live. (1952 address to the first International Congress of the Histopathology of the Nervous System)

Late 20th-century to today
In the latter half of the 20th century, movement against capital punishment became more pronounced around the world, and leading Catholics expressed their opposition as well.  The United States Conference of Catholic Bishops called for abolition in 1974, for example, and respected Franciscan Gino Concetti wrote against the penalty in 1977.
More recently, two popes in particular – John Paul II and Francis I – have made statements regarding capital punishment that seem, to some, to indicate a shift in the Church's view on capital punishment.  Feser and Bessette describe three positions in an ongoing debate in Catholicism: is it a reversal of traditional Catholic doctrine, a development of doctrine, or a prudential judgment of doctrine?  The different sides of this debate disagree on the strength of tradition outlined above (can it be contradicted by a pope?), and on the interpretation of the teachings of popes John Paul II and Francis.
Several significant landmarks of this period occur during John Paul II's papacy – the publication of the Catechism of the Catholic Church in 1992, the encyclical Evangelium Vitae in 1995, and the updated Catechism published in 1997.
In 1992, the Catechism upheld the legitimacy of the death penalty but argued for limited use of it:

For this reason the traditional teaching of the Church has acknowledged as well-founded the right and duty of legitimate public authority to punish malefactors by means of penalties commensurate with the gravity of the crime, not excluding, in cases of extreme gravity, the death penalty. [...]
If bloodless means are sufficient to defend human lives against an aggressor and to protect public order and the safety of persons, public authority should limit itself to such means, because they better correspond to the concrete conditions of the common good and are more in conformity to the dignity of the human person.

In 1995, John Paul II's encyclical emphasizes the content of this second portion, saying that cases requiring capital punishment today are "very rare, if not practically nonexistent," but never explicitly rejects the legitimacy of capital punishment.  This lead to an update to the Catechism, in which the first sentence quoted above is replaced as follows:

Assuming that the guilty party’s identity and responsibility have been fully determined, the traditional teaching of the Church does not exclude recourse to the death penalty, if this is the only possible way of effectively defending human lives against the unjust aggressor.

During the papacy of Benedict XVI, the Compendium of the Catechism of the Catholic Church was issued (2005).  It follows the 1997 catechism, and cites the "very rare, if not practically nonexistent" language of Evangelium Vitae, but again does not call the practice illegitimate.  Also in 2005, the USCCB published A Culture of Life and the Penalty of Death, reiterating its call for the abolition of capital punishment in the United States, and in 2009, a synod of African bishops supported universal abolition.
With the papacy of Pope Francis, the issue came to the forefront again.  He publicly expressed his support for the abolition of the death penalty in 2013 and 2014, and in 2015 used even stronger language:

Today capital punishment is unacceptable, however serious the condemned’s crime may have been. [...]  The death penalty is contrary to the meaning of humanitas and to divine mercy, which must be models for human
justice. (letter to the International Commission against the Death Penalty)

This has culminated in the 2018 revision to §2267 of the Catechism, which calls the death penalty "inadmissible" but uses language that suggests that support for abolition is at least partially based on the existence of "more effective systems of detention," and does not explicitly state that capital punishment is inherently immoral.  Additional explanation from the Vatican on this change is available in its Letter to the Bishops; it explicitly calls the change a "development of doctrine that is not in contradiction with the prior teachings of the Magisterium."
Summary
Through the years, the Catholic Church has consistently taught that the State legitimately holds the power of capital punishment, though its support for implementation of the practice has varied.  In recent decades, limiting and abolishing the practice has become a point of emphasis.  Some have contended that this represents a reversal of church doctrine, but the Vatican and others contend that it is a merely a development in doctrine.  Regardless, the practice has never been explicitly condemned as inherently immoral by an official publication of the Church, not to mention an ex cathedra statement.