You cast the copy while the ability is resolving and still on the stack. You can't wait to cast it later in the turn.

If you cast a spell by paying rather than paying its mana cost, you can't choose to cast it for any other alternative cost. You can, however, pay additional costs. If the spell has any mandatory additional costs, those must be paid to cast the card.

If you don't want to cast the copy, you can choose not to; the copy ceases to exist the next time state-based actions are performed.

If the spell has in its mana cost, you must choose 0 as the value of X when casting it by paying rather than paying its mana cost.