If you cast an instant or sorcery spell before Double Vision enters the battlefield during the same turn, its ability can't trigger that turn.

Double Vision's ability will copy any instant or sorcery spell, not just one with targets.

A copy is created even if the spell that caused Double Vision's ability to trigger has been countered by the time that 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. The new targets must be legal.

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 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.

The copy that Double Vision's ability creates is created on the stack, so it's not “cast.” Abilities that trigger when a player casts a spell won't trigger.