So I've been going through Menzoberranzan for a bit, and noticed some things the manual doesn't mention. Whenever I fight in cavernous areas (Leucrottas caves and descending into the Underdark so far) the weapons of certain companions are blacked out and are unable to be used. I thought it was an issue with Rangers, since it only happened to the Centaur and Drizzt (the Kenku can fight), but when I got this crazed Dwarf Cleric in descent lvl 2 to replace Drizzt, the dwarf doesn't seem to want to fight either. What is going on?

I also noticed a few weird things, like how I get a message on how the Centaur can't fire because of an empty quiver (despite the quiver being completely full and never seemed to deplete arrows). Is this a glitch?

From memory, the middle two characters are considered to be in the front row, which means that only they are able to use melee attacks in enclosed spaces. Ranged attacks from the back row should still work.

It's possible to move the characters around as well (I think clicking or right-clicking on their name will do it?)

Yes, give them a halberd or a quarterstaff and you're set.

I had the same problem, Drizzt won't use any melee weapons in caves or dungeons (which is the majority of the game). He can use bows or throwing weapons, but not melee weapons. Considering how tedious it is to pick up the arrows or throwing weapons used, I really don't want to use them except in special cases.
So there are two options: Either move Drizzt in the front line, or keep him in the back line and give him a halberd. I don't particularly like any of those options, but I ended up having him in the back line with a halberd. His special scimitars go to the two front-line characters.

Are you positively sure Drizzt is in the front row, Archimidis? If not, he'll need a long weapon to be able to fight in-doors: Aside from throwable stuff and bows, quarter staves, two-handed swords, and halberds can be used from the back row.

Note that if you previously played Ravenloft: Strahd's possession, the front row characters are now in the middle of the screen, and not the first two on the left.

Yes, that was my fault, I assumed front line was as in Reavenloft. I modified my previous post accordingly. Thank you Gotcha.

Take note where your starting characters are positioned in the beginning of the game. That is the front row.