Any spell you cast will be copied if you pay the cost, not just one that requires targets.

You may only pay the cost once, as the triggered ability resolves. You can't pay it more than once to get additional copies.

If a copy is created, you control the copy. That copy is created on the stack, so it's not "cast." Abilities that trigger when a player casts a spell won't trigger. The copy will then resolve like a normal spell, after players get a chance to cast spells and activate abilities.

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

If the copied spell 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. For example, if you sacrifice a 3/3 creature to cast Fling, and you copy it, the copy of Fling will also deal 3 damage to its target.

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, for one of the targets, you can't choose a new legal target, then it remains unchanged (even if the current target is illegal).