You can cast the copies in either order.

If the card has X in its mana cost, you must choose 0 as its value.

The copies are created in exile and cast from exile. The cards remain exiled.

The copy you cast first will already be on the stack when you cast the other copy. If that spell targets a spell, you may choose the first copy as a legal target.

If you cast a card “without paying its mana cost,” you can’t pay any alternative costs. You can pay additional costs such as kicker costs. If the card has mandatory additional costs, you must pay those.

If one of Spelltwine’s targets is illegal when Spelltwine tries to resolve, you’ll still exile and copy the remaining legal target.

Spelltwine has two targets: the instant or sorcery card in your graveyard and the one in an opponent’s graveyard. You can’t cast Spelltwine unless you can choose both legal targets.