If the exiled card is an Aura, that card’s owner chooses what it will enchant as it comes back onto the battlefield. An Aura put onto the battlefield this way doesn’t target anything (so it could be attached to a permanent with shroud, for example), but the Aura’s enchant ability restricts what it can be attached to. If the Aura can’t legally be attached to anything, it remains exiled.

If a token is exiled this way, it ceases to exist and won’t return to the battlefield.

If Glimmerpoint Stag somehow enters the battlefield during a turn’s end step, the exiled card won’t be returned to the battlefield until the beginning of the following turn’s end step.

The exiled card will return to the battlefield at the beginning of the next end step even if Glimmerpoint Stag is no longer on the battlefield at that time.