What of the West-Dwarves?
 

The Appendices state that after the destruction of Beleriand, the Dwarves of the two Western Houses in the Blue Mountains, the Broadbeams and Firebeards, fled east to Khazad-Dum, home of the Longbeards. Did they become permanently mingled with Durin's Folk, or did they return to the Blue Mountains in later Ages to re-colonise the lands of their Fathers? Among the Dwarves of Thorin's company Bifur, Bofur and Bombur were not of Durin's Folk, so it seems that they may have maintained their separate identity. Thoughts?

Very interesting questions. I do not know that I have any answers. I imagine there was some intermingling, and I also would imagine that a remnant returned to the Blue Mountains.

Merry

Great question. I have come to the conclusion that the majority of the FBs and BBs (Firebeards and Broadbeams) went to the newer dwellings of their kinsman in the Blue Mts, who though few had dwelt their since the Fall of Beleriand even though most of their people left for Khazad-dum. Those lands were much more peaceful than the realms of the Dwarves of Durin's folk. While a small amount stayed with Durin's folk.
They possibly were leaving even before the awakening of Durin's bane, since the dwindling of the population Khazad-dum wasn't necessarily death.

Afterwards Thrain was captured in 2841 east of the Anduin and imprisoned in Dol Guldor where Gandalf found him in 2850. We can assume that a small amount of Dwarves lived there for at least 51 or so years.

I assume this means the Ered Luin.

Again, I assume the reference to Eriador to be the Ered Luin, but I am thrown off by it stating to a certain extent "They laboured long and had fair halls" implying that they were new and would not be the ancient mansions of Nogrod and Belegost...

There is alot more information but I am too sleepy. :D

There still were some in the Third Age in the south of the Ered Luin and these were probably either descendants of those that never left the area or of those that fled after the awakening of Durin's Bane.

Both from the Appendix.

So first it's said that the people of Khazad-dûm fled far away and then that Durin's folk was gathering in the north. So what about the others?
Maybe they decided to go back to their ancestral homes and split up with Durin's folk.

They clearly would have had contact to Thráin and so some went with him on the quest.

Quit right Imperica. Infact, if I'm not mistaken, I believe all of the thriteen dwarves with Bilbo were from the Blue Mountains.