A copy is created even if the spell that caused the delayed triggered ability to trigger has been countered by the time that delayed triggered ability resolves. The copy resolves before the original spell.

The copy will have the same targets as the spell it's copying unless you choose new ones. You may change any number of the targets, including all of them or none of them. If the spell is a permanent spell with targets, such as an Aura, you may also choose a new target for that spell. The new targets must be legal. If, for any target, you can't choose a new legal target, then it remains unchanged (even if the current target is illegal).

The copy is created on the stack, so it's not "cast." Creating the copy won't cause abilities that trigger when a player casts a spell to trigger.

If the spell that's copied is modal (that is, it says "Choose one —" or the like), the copy will have the same mode or modes. You can't choose different ones.

If the spell that's copied has an X whose value was determined as it was cast, the copy has the same value of X.

You can't choose to pay any additional costs for a copied spell. However, effects based on any additional costs that were paid for the original spell are copied as though those same costs were paid for the copy too.

If the spell has damage divided as it was put onto the stack, the division can't be changed, although the targets receiving that damage still can. The same is true of spells that distribute counters.

Any choices made when the spell resolves won't have been made yet when it's copied. Any such choices will be made separately when the copy resolves.