As to your first question, the business is welcome to send you the bill for restitution, just as you are free either to pay it or ignore it. If there has been no adjudication of guilt and sentence ordering you to pay restitution, though, you are under no court-ordered obligation to pay.
You asked the right question to the detective. If you are not under arrest, you have no obligation to speak with him and shouldn't. He is completely allowed to TRY and get you to talk, but you are completely allowed to do what you did and tell him to go away or arrest you. It seems like you have done a good job of protecting your rights thus far, so the next important step is for you to find a lawyer to help you through whatever you are dealing with at the moment.
It sounds like what the business did is send you a civil restitution document. Yes it is legal but most lawyers will tell you to ignore it. It is very unlikely that you will be sued for the restitution. When you hire your criminal defense lawyer, talk to him/her and let them know about the letter you received.
Criminal defense Criminal charges Drug related crimes Criminal charges for vandalism Criminal conspirator Criminal charges for probation violation Defenses for criminal charges Criminal arrest Criminal sentencing Victim compensation and criminal conviction Federal crime Violent crime Civil rights