Does the other party's attorney have to let me do a payment plan? Or if I lose at court will the court repossess my car and all my belongings?

I gather you don't have insurance (if you do notify your insurance company right away) and are talking about a potential settlement of a claim which has not yet been litigated  If so, you should know that settlements are voluntary agreements and nobody is required to agree to anything.  If you go to court and lose, a judgment will be entered against you.  IF you don't pay that judgment, or agree on a schedule for paying it off, the plaintiff, now a judgment creditor, will avail himself/herself of various procedures to collect on the judgment, which could include seizing and selling your assets to pay down hte judgment.  Some assets are exempt from this procedure, but you will have to check the extmptions in California (I'm sure you can look them up online) to see what assets would be exempt.