Similarly, you may ask, can you gain control of a creature you already control?
Act of Treason can target any creature, even one that's untapped or one you already control. Gaining control of a creature doesn't cause you to gain control of any Auras or Equipment attached to it.
Beside above, do you control cards in your graveyard? Objects that are neither on the stack nor on the battlefield aren't controlled by any player. Effects that deal with cards in the graveyard would refer to their owner.
Also to know, when you gain control of a creature does it have summoning sickness?
Yes, a creature gets summoning sickness after taking control of it. 302.6.: A creature's activated ability with the tap symbol or the untap symbol in its activation cost can't be activated unless the creature has been under its controller's control continuously since their most recent turn began.
What happens to equipment when creature dies?
What happens to equipment attached to a creature when the creature dies? Nothing. It stays on the battlefield, not equipped to anything. If you steal a creature that has an equipment equipped and it dies you don't keep the equipment though.