When an effect returns the exiled card “under your control,” you control it indefinitely after that. In a multiplayer game, if a player leaves the game, all cards that player owns leave as well. If you leave the game, any creatures you control from Conjurer's Closet effect are exiled.

If you gain control of a creature “until end of turn,” you control it during that turn's end step.

If a token is exiled this way, it will cease to exist and won't return to the battlefield.

Once the exiled creature returns, it's considered a new object with no relation to the object that it was. Auras attached to the exiled creature will be put into their owners' graveyards. Equipment attached to the exiled creature will become unattached and remain on the battlefield. Any counters on the exiled creature will cease to exist.