The cards are exiled face up.

The once-a-turn restriction of the last ability applies only to nonland cards. You can play a land card exiled with Hedonist’s Trove on the same turn you cast a nonland card exiled that way.

Playing a card this way follows the normal rules for playing the card. You must pay its costs, and you must follow all applicable timing rules. For example, if one of the cards is a creature card, you can cast that card only during your main phase while the stack is empty.

Under normal circumstances, you can play a land card exiled with Hedonist’s Trove only if you haven’t played a land yet that turn.

If Hedonist’s Trove leaves the battlefield, any cards it exiled remain exiled. Those cards can no longer be played. Any future instance of Hedonist’s Trove (even one represented by the same card) will be a new object and won’t allow you to play those cards.