[MvCrash]

To fill in on some answers posted: (NJ)

A. ANYONE can sign a motor vehicle complaint against ANYONE. The only difference between a civilian signing the complaint and an officer signing the complaint is that only an officer of the court can serve the SUMMONS portion. (which compels you to court or pay a fine unless court is mandatory) So if you, a civilian, wish to sign a MV complaint, go to your local police station and let them know, they SHOULD walk you through the process and then either deliver the summons themselves or have the court serve the summons through the US mail or other means.

B. You insurance company is responsible to pay your damages. THEY have the right (read the policy) to pick payment or replacement. If you do not like the settlement you have the right to an independant adjuster, and an attorney to file a civil complaint to recover your damages. And yes, they have to pay the attorney to represent you.
As far as damages to the car, once your insurance company decides it is not your fault, they will subrogate the claim to the other insurance company to recover their loss. They will also get your deductible back and mail you a check.

Hope that helps.