Legal Question in Personal Injury in California

No

You cannot sue an insurance company that is not YOUR insurance company for anything. The only thing you can sue an insurance company for is for wrongfully declining coverage under a policy on which you are an insured party.

You can sue, but you can't win. Insuring an unlicensed driver did not breach any duty that the insurance company owed to you. It also didn't cause you any injury.

Great question.... I once asked a lawyer that did class actions cases the same question. It seems that that it encourages people who are not licensed to drive. The answer was that there was no reason to sue because it is not illegal to insure unlicensed drivers and it benefits the public because at least those people are financially responsible. It does seem odd that a person who is unlicensed can be insured to drive in violation of the law. This is something for the legislature to consider as public policy.

No. You have no legal relationship with the insurance company. Any claim you have would be against the driver and registered owner[s] of the car, if they caused you damage. There is no requirement of a license to buy an insurance policy to cover the car..