I am a CA lawyer.  The way you tell descibe the incident, I think you are negligent.  You were following too closely and/or traveling too fast for the conditions.  The driver of the SUV has a claim he/she can make against you for the damage to the rear of their vehicle.  Sorry.  Glad to hear that no one was hurt.

Yes you can, because California has comparative negligence. Your damages would be reduced by the percentage of fault attributed to you. It could be that if the SUV did not brake and you had no warning of their abrupt stop, then you might not be as negligent as other people think and that is why you should see a personal injury attorney. Even though the police officer said its was the SUV’s fault his opinion is not admissible court too bad he didn’t write up a report. Even though the reports are likewise inadmissible everyone commonly goes by in trying to settle a case.

Good to hear you weren’t injured. I’d let your insurance carrier handle the claim. If you didn’t have collision coverage take them to small claims court recovery limited to $5K or less though.

Hope this helps and good luck to you.