Playing a card exiled with Fiend of the Shadows follows all the normal rules for playing that card. You must pay its costs, and you must follow all timing restrictions, for example.

As long as the card remains exiled, you may still play it, even if Fiend of the Shadows leaves the battlefield or changes controllers.

If this creature deals combat damage to multiple players simultaneously, perhaps because some combat damage was redirected, its ability will trigger for each of those players.

You may only play the card, meaning play it as a land or cast it as a spell. It's not in your hand. You can't discard it, activate its cycling abilities, and so on.