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 or ability are copied as though those same costs were paid for the copy. For example, if you sacrifice a 3/3 creature to cast Fling and then copy it with Wyll's Reversal, the copy of Fling will also deal 3 damage to its target.

If the target spell or ability is modal (that is, it has a bulleted list of choices), the copy will have the same mode(s). You can't choose different ones.

Even though you do not gain control of the original spell or ability, you control the copy. That copy is created on the stack, so it isn't "cast." Abilities that trigger when a player casts a spell won't trigger. The copy will then resolve like a normal spell or ability, after players get a chance to cast spells and activate abilities. The copy will resolve before the original spell or ability.

If the spell is a permanent spell with a target (such as an Aura spell), and you create a copy of it, the copy will become a token that you control. Because the spell becomes a token, the token isn't "created." Effects that care about a token being created won't interact with a token that enters the battlefield because Wyll's Reversal copied a permanent spell.

The copy will have the same targets as the spell or ability 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).

If the target spell or ability has an X whose value was determined as it was cast, activated, or put on the stack (like Fireball does), the copy has the same value of X.