Parking car was rammed – what now?

Moin! My girlfriend’s parking car was rammed by a second car a few days ago while parking. The opponent was a rental car, the incident was seen by two witnesses and kindly they left us a note on which they described the incident and left their number. Of course, the causer made a hit, although the impact was so severe that the rammed car moved clearly. A big surprise: you have to get around EVERYTHING se My question now: what about an expert? Do you have to accept the insurance policy of the opposing party or can you propose your own and, above all, independent insurance policy? If so, who pays for it? The debt issue should be clear even in our state of law. Do you also have to accept that the insurance expert will take X weeks until he has time? Or can you set deadlines? I would be grateful for a brief information.