You can cast the copy only as the triggered ability resolves. If you don’t want to cast it at that time (or you can’t cast it, perhaps because there are no legal targets available), the copy ceases to exist. You can’t cast it later.

The copy of the card is created in exile and cast from exile, not from a graveyard.

The chosen player chooses which card to exile from their graveyard.

You can cast the copy during the resolution of the triggered ability if it’s a sorcery, no matter whose turn it is or which phase it is.

If a spell has in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.

If you cast a card “without paying its mana cost,” you can’t choose to cast it for any alternative costs. You can, however, pay additional costs. If the card has any mandatory additional costs, such as that of Momentous Fall, you must pay those to cast the card.

You choose a player at random and they exile a card all while the triggered ability is resolving. No player may take any actions between the two or between exiling the card and you copying and casting it.

If the chosen player has no instant or sorcery cards in their graveyard, Wildfire Devils’s ability does nothing. You don’t pick a different player.