Yes, you have to pay your parking tickets. If you fail to pay parking tickets you won't be able to register your vehicle with CA DMV until you do. Parking tickets are a revenue raising scheme but there's no way to avoid them unless you have diplomatic immunity. Good luck.
The tickets will go against the registration of the vehicle, and you will not be able to register it if you don't pay. You can contest them as well, read the back of the ticket.