If a creature has an ability that triggers at the beginning of each end step and Trostani's ability causes you to gain control of it, the ability of that creature is still controlled by the creature's former controller. If the creature has an ability that triggers at the beginning of your end step, that ability doesn't trigger when you gain control of it.

The owner of a token is the player who created it.

Because damage remains marked on a creature until it's removed as the turn ends, nonlethal damage dealt to other creatures you control may become lethal if Trostani leaves the battlefield during that turn.