Got into an accident yesterday, someone hit the rear side door while it was fully open with his side window, which popped the rear door past it's hinge into the front left door - The door hinge now feels very flimsy / broken, and theirs some dents and damaged pieces. Other guy seemed to understand he had messed up. Not sure what to do next.

1. Do I call my insurance or the other persons? (I have Collision / Comp coverage) - After this what happens?
2. This happened when I was legally parked at the side of a street - Am I partially at fault here?
3. Should I take this to Mbenz for repairs or somewhere else?
4. How long is it likely going to take to fix something like this and how much likely to cost?
5. Any other tips that will help to get it fixed ASAP and ensure the repairs are high quality?
6. Is it worth me getting a quote somewhere and offering the other guy to pay cash instead of going through insurance? - Seems like this could be less of a headache if he agrees
7. Overall how long can I expect the whole process to take?

I'm in the USA (California) - I have some video footage immediately following the incident which shows the damage to my car and the other car - I also have the plates for the other guys car and his insurance info

Any help / tips / outline of the claims process is greatly appreciated!

Sorry to hear! As nobody was hurt, I would definitely call your insurance company first. They should tell you all the next steps.

Cal your insurance ASAP and tell them everything.
police report? need the # for your insurance as they will be your backup and no matter what the driver said his insurance will fight it as that is their job.