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

If you cast an instant or sorcery spell that has multiple targets, but it's targeting only Zada with all of them, Zada's ability will trigger. The copies will similarly each be targeting only one of your other creatures. You can't change any of the copy's targets to other creatures.

The copies that the ability creates are created on the stack, so they're not cast. Abilities that trigger when a player casts a spell (like Zada's ability itself) won't trigger.

Zada's ability triggers whenever you cast an instant or sorcery spell that targets only Zada and no other object or player.

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

Any creature you control that couldn't be targeted by the original spell (due to shroud, protection abilities, targeting restrictions, or any other reason) is just ignored by Zada's ability.

If the spell that's copied has an X whose value was determined as it was cast (like Rolling Thunder does), the copies have the same value of X.

You control all the copies. You choose the order the copies are put onto the stack. The original spell will be on the stack beneath those copies and will resolve last.