When I exile a manifested permanent like an enchantment or creature with something like Roon of the Hidden Realm, it comes back face up (from what I understand). What happens if I exile and return an instant, sorcery or aura enchantment? Do their effects take place on the end of my turn?
Instants and sorceries would stay in the zone they're currently in, in your case in Exile. They do nothing.
304.4. Instants can’t enter the battlefield. If an instant would enter the battlefield, it remains in its previous zone instead.
307.4. Sorceries can’t enter the battlefield. If a sorcery would enter the battlefield, it remains in its previous zone instead.
If an Aura enters the battlefield other than by resolving, you can choose a legal object or player for it to enchant. Note that this does not target the chosen object. If you can't because there are no legal objects to enchant, it remains in the zone it came from; in your case, in Exile.
303.4f If an Aura is entering the battlefield under a player’s control by any means other than by resolving as an Aura spell, and the effect putting it onto the battlefield doesn’t specify the object or player the Aura will enchant, that player chooses what it will enchant as the Aura enters the battlefield. The player must choose a legal object or player according to the Aura’s enchant ability and any other applicable effects.
303.4g If an Aura is entering the battlefield and there is no legal object or player for it to enchant, the Aura remains in its current zone, unless that zone is the stack. In that case, the Aura is put into its owner’s graveyard instead of entering the battlefield.