Sure. You might have to go the Calif. Secretary of State's website to find out how to serve your insurance company. But sue them in small claims court. They will probably pay to avoid the hassle of having to appear and defend the case.
Yes, you can sue your insurance company for denying your claim.
You can find general information about how to file a small claims lawsuit at:
Frank W. Chen has been licensed to practice law in California since 1988. The information presented here is general in nature and is not intended, nor should be construed, as legal advice for a particular case. This posting does not create any attorney-client relationship with the author. For specific advice about your particular situation, consult with your own attorney.