Got in a wreck for the first time yesterday

I was trying to leave a coffee shop and there was a vehicle that from what I could tell from the angle, was parked near the curb and there were people standing outside of the vehicle with a door open. They were partially blocking the driveway but I had room to go around them to get out on the main road. Not even 10 seconds after I pull up (I am stationary, my foot was on the brake waiting for oncoming traffic to clear) so I could turn right onto the main road, the vehicle accelerates and hits me.

Police were called but they couldn't file a crash report since it was on private property. I exchanged insurance information with the other driver and also got the number of a witness. The witness who saw it happen said the driver of the other vehicle was at fault. The daughter of the driver (same woman was standing outside when I first saw the vehicle) insisted it was my fault.

I have multiple photos of the wreck and I also was able to obtain footage from a business showing the collision, but it's not the best angle and my husband is worried that the insurance company will try and put me fully or partially at fault and say I should have tried to go out of a different exit in the same parking lot. I am waiting to hear back from the other business with a closer camera to see if I can obtain that footage.

I guess my questions are, 1) should I send the footage to the adjuster as soon as one is assigned or do I wait and see if the other driver admitted fault if it's as obvious as everyone keeps telling me it is from the photos? and 2) how soon can I hope to get in a rental car until my car can be assessed? both me and the other driver have Progressive if that helps!

Edit: I added a photo in the comments (covered all identifying information)