Barazinbar is the Redhorn mountain, or Caradhras as it is known in Sindarin. It is one of the three mountains of Moria, being the northernmost and tallest. The Dwarves referred to it simply as "Baraz" for short. Karen Wynn Fonstad notes in The Atlas of Middle-earth that Barazinbar may have had mineral deposits that differed from the surrounding foothills and mountains which gave it a reddish hue.
In each source of this name, Tolkien says that baraz is "probably red or ruddy". That would make this word an adjective. Because it shows up as the first element in the compound, it is also most likely in the composition form, parallel to Khazad-dûm. However, the normal, indefinite state is probably not barâz like you would see for Khazâd, seeing as how that is a plural. If the indefinite were bâraz, then in the composition form the long Â vowel would reduce to a schwa, either ë or ü following the orthography I have determined for this site. That is, the composition form would be bëraz or büraz. It's possible that the first A in baraz is actually a schwa sound. However, the CaCaC pattern is found elsewhere in Tumunzahar, where it would not be in composition form, and in Narag-zâram. The word narag apparently gets further reduced to narg- in Nargûn, which to me indicates that the first syllable is probably stressed, rather than the second. If that's the case, then it's less likely that the first A in baraz is unstressed, and therefore gets reduced in composition. Following that, the easiest interpretation here and with the other examples is that CaCaC is a valid pattern in Khuzdul, and is commonly applied to adjectives.
In my opinion then baraz is "red, ruddy" and singular, nominative, composition.
Also in the glosses of Barazinbar, Tolkien gives a translation for inbar of "a horn". He explains by saying that Barazinbar "seems to have been a great mountain tapering upwards (like the Matterhorn)...". It is interesting that in The Treason of Isengard, pg 174, the radicals for inbar's root are given as M-B-R. In Arabic, /n/ is assimilated to /m/ when next to a /b/. Additionally, Tolkien usually has /n/ assimilating to /b/ in most of his languages, including Adunaic. The Angerthas even has #7 as a value of MB, showing its commonality. It would be odd for the radicals to be M-B-R and then see a dissimilation from imbar to inbar. However, it is noted in Parma Eldalamberon XVII, pg 35, that "the base for inbar was given incorrectly as MBR." We can probably say that the root is indeed N-B-R, and the N probably assimilates to M in spoken Khuzdul (as though it were imbar) but isn't reflected in the writing.
Another noteworthy feature of inbar is its vowel patter iCCaC. In Appendix F of The Return of the King, Tolkien says that Angerthas #35 is " ' (the clear or glottal beginning of a word with an initial vowel that appeared in Khuzdul)", which we know matches with Semitic syllable structures. The glottal stop, ' , is considered a unique consonant in Semitic languages. In Arabic, it is not uncommon for word templates to use a pattern that starts with a glottal stop and then includes the root consonants afterwards. As an example, a common plural pattern there is 'aCCâC. When writing inbar by itself, we should technically write it as 'inbar. However, Tolkien himself seems to have never done this at all, so I don't think we need to stress about it. In any event, it can be noted that when inserted into a compound word, the glottal stop is removed, so we get Barazinbar instead of Baraz'inbar.
Tolkien never refers to inbar as anything but "horn", and since it refers to a mountain, it is quite surely singular in number. Also, since it is the second element, it should be in the indefinite state, not composition.
Inbar then should be "horn" and singular, nominative, indefinite.
Barazinbar is thus a compound word, showing an adjective-noun word order.
The Lord of the Rings, The Fellowship of the Ring, Book II, ch 3
The Lord of the Rings: A Reader's Companion, pg 267
The Treason of Isengard, pg 174, 432
Parma Eldalamberon XVII: Words, Phrases and Passages, pg 35