Title is self explanatory for the most part.

I took some gear off of my merc and it seemed like it was degrading. I play on hardcoe.

Does it degrade if you equip them with gear and they use that equipment or is this in my imagination ?

I was wondering about that myself, hoping somebody could answer. I found T-51b BOS armor that I gave to Veronica, and it hasn't seemed to degrade, however I gave her Nehri's driver to use, which she equipped as opposed to her power fist. Later on I realized she was no longer using it and it had disappeared from her inventory. Even if it was at 0% condition, shouldn't it still be in the inv? I was kinda miffed at losing a unique weapon in the game. And apparently, companions use up ammo as well? Anyone confirm this?

I'm not sure, I haven't noticed this. I have noticed that companions need ammo for weapons that they did not start out with, though. Wouldn't be surprised if companion armor does have to be repaired.

Companions use ammo for anything that you give them. The weapon that is their default does not run out of ammo. If you give them a weapon you must give them ammo so it is easier to pick the Companions that have good weapons because they won't run out of ammo for their Hunting Rifle or whatever they are using. Any equipment that they are wearing/using will never degrade. Companions die in hardcoe but only go unconscious in Casual. Companions cannot use modded guns.

Don't trust Boone or Veronica they'll steal your [censored] and act stupid by giving you the same, go nowhere, dialogue when you talk to em. ED-E too , he stole my 9 so i shot him twice in his central processor and once in his memory bank and he's dead forever!

That is really interesting you said that. I had a "oh baby!" unique hammer on veronica, I noticed she was using her power fist. When I looked in the inventory the hammer was gone. I panicked and then re-loaded a previous save and took the hammer off of her. I looked at the level of repair degradation and it was really low || much left.

I had picked it up and never used it at all until I gave it to her when I originally found it. I cannot remember what the original level of degradation is on the "Oh baby!" unique hammer. If my memory isn't deteriorating I think I got the hammer when it was at around 50% so I duno. Maybe its a bug for veronica. I can't recall any degradation happening on boones equipment but maybe I just didn't notice it.

In FO3 armor/weapons given to a follower to not degrade with one exception.

Weapons given to your follower will suffer damage if the weapon itself is hit during combat (i.e. a raider shoots the Cowboy repeater you gave Boone, thus damaging it).

I can only assume this is still true in New Vegas.