If more then half of your tire tread is visable when looked at from the rear, you need mud flaps on the street in California. Read the V.C. it can be found on the State of Calif. DMV web page.
No doors is a judgement call on the LEO's, some say yes, some say no. I have asked at least a dozen LEO's about and get different answers. If they really want to get sticky they can always say it is an unsafe vehicle, impound it on a thirty day hold and in order to get it back you pay the tow fee and impound fee. Then you pay the fees and if you have been a SA to them they are waiting for you as you drive out of the impound yard and they do it all over again. It is hard but not impossible to beat the MAN. In the words of Patrick Swayze in the movie Roadhouse, "Be Nice" as much as you do not want to be, it works.