Sacramento

There's a couple of things to think about. With the value of damage and your deductible, the most you would save by filing a claim is 2k.

Yes, you can get insurance without a license. There will be a surcharge for not having a license in California.

Insurance companies are regulated at a state commissioner level and in theory, are supposed to be neutral. But, it's hard to say for sure any being is entirely neutral.

In most cases insurance companies do give you a window to transfer a new vehicle to your plan. In my experience the policy will match the same coverage for up to 14-30 days that your plan currently provides for the vehicle you are replacing.

Compensation is normally paid by the insurance company of the at-fault driver if you have to go to the doctor/hospital or if you have to miss work. You'll need to contact their insurer to begin the process unless you don't plan on getting medical attention for your injuries.

Unfortunately, you would be filing a collision claim which would be categorized by your insurer as an at-fault accident. This will likely cause your rate to increase.

You should be able to request a copy of the report from the highway patrol since they should have a record of it. As for filing a claim, that decision will be completely up to you, but you will likely be charged for an at fault accident since no other vehicle was involved.

You could claim the damage as a hit-and-run, but that's technically not what happened so I would avoid lying to your insurance company. I would recommend getting a repair estimate first so you can factor that into your decision.

Unfortunately there really isn't much that you can do. Even if the other driver is found to be at fault, without them having insurance your vehicle is pretty unlikely to get fixed unless you pay for the repairs yourself.