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

The copy created by Cursed Recording's last ability 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. The new targets must be legal.

The copy made by Cursed Recording's last ability is created on the stack, so it's not "cast."

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.

You can't choose to pay any additional costs for the copy. 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.