Opponent controlling me

[Avodroc13]

When an opponent controls me and makes my decisions, etc. Can he unequip equipment from my creature and equip it to his? Then when it's his turn again use my equipment against me?

When it's my turn can I unequip it from his creature or do I have to destroy it?

One other thing, if I had {Elixer of Immortality} out, and they controlled me and used it, would they gain life and shuffle their graveyard into their library?

[TheRagingMage]

Artifacts can not be attached to opponent's creatures:  702.6a: Equip is an activated ability of Equipment cards. "Equip [cost]" means "[Cost]: Attach this permanent to target creature you control. Activate this ability only any time you could cast a sorcery."
With {elixir of immortality}, you would gain the life and you would shuffle your graveyard into your library.  He gains control of you, not your spells and abilities.

[LinkCelestrial]

Another way to word this is that he is you, as he is controlling you. So if he activates {Elixir of Immortality} it's like you activated it therefore you gain the life and shuffle.