Restitution

Yes, they can do this.  You might want to look into getting a loan to pay this off, it might end up being cheaper, depending on those fees.

Your restitution is a judgment against you, just as if you had been sued in civil court for whatever damages you caused.  But since this is a criminal case, it isn't up to the person who was harmed, who would have been the civil plaintiff:  the "plaintiff" in your case is the State.  You can ask the court for a modified sentence, but you would need to show some very good reasons why you should be let off the hook.