I feel like this is a stupid question, but I have to ask anyway.

Does giving your companion better armor and weapons actually increase their performance? If so, do they make use of any enchantments on their gear?

I really don't know, but I gave Lydia a weapon and she uses it now and it's stronger than her other one.

I haven't given my companion enchanted armor yet, but he does have a soul trap war axe that definitely works.

I gave two frost staffs to my companion and it equiped both at the same time Better armor means more protection for them too. I also gave a necklace with huge fire resistance and a helmet with 30% resistance to all elements, meaning a fire user will be screwed against my companion. An enchanted elven waraxe turned out to be better to give than two staffs and now she's rolling with those. A true killing machine!

May I ask how it works? Does it fill a soul gem that you are carrying, or do you have to give your companion a bunch for themselves?

He's carrying all my empty soul gems, yeah. The thunderclap/swirly animation definitely goes to him instead of me as well.

I do and i actually find that giving Lydia a weapon with an enchantment, the enchantment always works and never runs out. Pretty helpful actually.

OP: oh yes, it does. I've been giving Jenassa better elven/glass armor and also gave her two staves which she wields all bad ass!

That's nifty. I'll have to keep that in mind.

I noticed at least Lydia will only wear head armor that i gave her, but will use weapons. They will use the last item for htat slot that you hand them, remember that.

I don't think that's true; I've definitely given my companion a bunch more weapons but he still prefers the aforementioned soul trap axe best. I think it functions much like the armor, in that if it's better than what they've got at the moment, they'll use it.

I don't think this is right, my companion's weapon is also enchanted but it definitely run out and I have to refill it, I'm guessing either the enchanted weapon that you gave has a large amount of charges so it goes down very little (and the fact that in most cases you'd most of the hitting while your companion only help out so they'd actually take off little charges from their enchanted weapon)... but I'm pretty sure your companion's enchanted weapon will run out of charges eventually. Now if anyone can help me, do your followers use any potions that you give them (and if they use it conservatively?)

oh wow thats a great idea, thanks
cause im to lazy to refill empty soul gems lol

Yes

I gave Lydia a staff that summons things and she started being my personal summoner.

Does anyone know how to get rid of Lydia's hunting bow? I gave her an elven bow. She wields that for a brief period until I sheath my weapons. Then when the fight starts again she just switches to her hunting bow again

Yes, and enchantments work with them as well.