Casting an exiled card causes it to leave exile. You can't cast it multiple times.

Any cards not cast, including land cards, remain in exile.

Apex of Power doesn't change when you can cast the exiled cards. For example, if you exile a sorcery card, you can cast it only during your main phase when the stack is empty.

If an effect copies Apex of Power, the copy wasn't cast at all, so you won't add ten mana.