Read the Cal-Code here: http://www.cdph.ca.gov/services/Documents/fdbRFC.pdf
That being said, different counties may have stricter guidelines. But "generally" to call yourself a "caterer" you have to have a commercial kitchen. Some counties you can call yourself a "cook for hire" and be ok as long as all food is bought same day, prepped and cooked on-site. Check with your local HD for clarification.
As far as competition, it is an expensive "hobby" and not one to jump into blind. 7 months ago we (wife and I) attended our second ever comp by volunteering in the judges tent. We were hooked. Joined KCBS and CBBQA, got our judges badge, have met some great folks through both organizations and learned a lot. i am glad I didn't just jump right in and enter a comp. It would of been a complete failure. Take a similar path, get to know the right people, and learn the process first!! Incidently, Aug 10th we cook our first comp type event. A KCBS licensed (as opposed to sanctioned) backyard event in Ontario. Great way to get the feet wet, and plan on our first pro comp around Jan 1st.