Can I apply here in trinidad holding a British Passport

I am starting a job in China , I have an invitation letter and I hold a British passport whilst I am working here in trinidad . Can I apply in the local Chinese embassy .

My girl friend I want to bring with me , do I have to buy a round flight ticket before a visa is granted ? If so what happens if the visa is not granted the Airline round trip tickets are hard to find with out transfers through London