In general, not ca specific, but in order to get your biz Lic you will need general liability insurance. And in order to get these you will need to deal with the health department and have a licensed kitchen to prep food in. I have heard ca is tougher than most states. Keep in mind at least here the HD is county based and all biz permits/lics are city based. So you need to reach to each of these you plan vending in. Some states allow for temp permits for a few events a year and the HD will inspect your setup at the event, but once you apply for the limit of permits you are done for the year or you need to go pernement. One more thing our city required a 1k surety bond to pull the permit along with proof of ins and HD inspection approval. In my case my operating permit is in the works approval and pending HD inspection once the trailer is finished.
Hope this helps
Ole Hickory EL IB, WSM 18 & 22, Jacks Old South insulated, Weber Preformer