You choose which opponent chooses the pile while resolving Abstract Performance.

You cast the spell while Abstract Performance is resolving and still on the stack. You can't wait to cast it later in the turn. Timing restrictions based on its types are ignored.

If you have fewer than eight cards in your library, the second pile will be smaller than the first. If you have fewer than five cards in your library, only the face-down pile will have cards in it at all, and the second pile will be empty. In that case, your opponent will probably choose to put the pile with cards in it into your graveyard.

If you cast a spell "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, you must pay those to cast the spell.

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

You can't look at the cards in the face-down pile until you're instructed to do so or until they're moved to the graveyard (at which point they'll be face up).