If you give your follower an enchanted weapon and they use it, does it drain its power like if the player charecter used it?

Yes, they drain power and need to be recharged to be active.

Both Lydia & Aela use the staffs I give them like crack. I waste more soul gems on those two. Seems staffs become their favorite to use....

They do but it doesn't appear to drain as fast as for me. I recharge Lydia's stuff once in a while but often don't need to. I might recharge my stuff 10 times before hers

Followers will apparently default to staffs over any other weapon they have in their inventory, regardless of damage or skill stats. I had to take a lightning staff away from Erik the Slayer because he kept using it instead of his giant, specially enchanted dwemer battleaxe. Also he kept hitting my character with the lightning bolts.

Yes, Jenassa has been using an enchanted axe and has gone through the charges pretty rapidly.

Not to mention completely wasting a staff by using it against the lowest level enemies. It never stops being frustrating when Lydia wastes a bunch of fireballs on mudcrabs that I am bypassing with no intention to fight them anyway. Then when I get in a fight against a group of thougher enemies she has no charge left in the staff.

Mjoll has taken a liking to the staff of fireballs I forgot I gave her. Went into battle, then was like 'WTF?!' as something exploded and I thought I was being attacked by a mage. Nah, just Mjoll, staff in one hand, sword in the other.

I try to be careful when assuming my follower will carry something instead of using it.

Yes I gave my follower, Brelyna Maryon, the staff of Magnus and she uses it on everything and I'm having to recharge it (takes a lot of charges) all the time