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

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 Isochron Scepter leaves the battlefield while the activated ability is on the stack, the ability can still make a copy. On the other hand, if the imprinted card leaves the exile zone while the activated ability is on the stack, the copy can't be made.

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, those must be paid to cast the spell.