Probably a bit silly of me to have to ask, but please be patient.

1) Does the durability of companions' gear degrade when used? Does it need to be repaired?

2) Do I need to keep them stocked up on ammo, or does the "magic companion ammo" apply to the guns they're given?

3) What's the logic of the companions' weapons preference? Do they go for highest DAM, highest DPS, a specific class of weapons associated with that particular character?

4) Do they have a default preference for ammunition types? (AP, JHP, normal shotgun shells vs. slugs)?

5) Do followers benefit from weapon mods such as as scopes and silencers?

1 - Well, the best answer to that is....sometimes. I don't think weapons degrade from use, but they can be damaged by gunfire/splash damage, even to the point of them dropping the now-broken weapon (not often). Typically their armor rarely takes any damage, but their weapons do a bit more often.
2 -Yes, companions need ammo for any weapon you give them. Their default is the only one that never runs out of ammo
3 - My experience says it's the DPS they choose from. (edit)And how they determine the DPS seems based on THEIR current skills, not yours. Which is why sometimes they switch back & forth from one ranged weapon to another sometimes (or 2 diff. melee)...their skills are such that the two weapons are almost identical DPS and I think they get confused which to choose.
4 - My experience says there's no preference per se, however if you have both 5.56 regular and 5.56AP in their inventory, they will use up the non-AP entirely first. So if you want them to use the 5.56AP, you have to remove the other types.
5 - Sadly....no. (edit) Want to clarify - they will benefit from fire rate, bigger magazine type weapon mods. But the silencer...no. Scope...not that I can tell.

Do they also prefer JHP over AP and normal?

That I do not know, since I never use handloaded/special ammo. One person posted that they couldn't get them to use certain ammos at all, but I have no idea if that's a bug or not. If I were to make a guess, however, I'd say that companions are geared to use the least expensive/effective ammo, so to speak, first, as an attempt to conserve it for the player in case the player isn't aware/didn't want them to use it. Just a guess. Put some in their inventory and find out.

They do switch weapons under different conditions. There is some kind of simple AI behind it. In my experience range to target seems to play role as well. Bone for example switches from his rifle to melee weapon or 10mm SMG when opponent gets close. Or he used to before patch at last, I started new game after patching so I did not get him so far.