What documentation is required to exit Mainland China on good terms

I would like to know the proper documentation and requirements to exit Mainland China. I am a USA citizen and my passport is gone. At the US Embassy in Guangzhou they said that they could issue me a limited passport for a direct flight to the USA. Do I need a China visa put on this document in order to exit properly and on good terms?

My old US passport contained an F visa valid until September 2011 with 30 day departures. My next scheduled departure is May 19th. I have a temporary residence certificate that is valid until this date (it gets renewed each month in Zhuhai at the local police station). Going back to the USA before the 19th is possible if I schedule the flight and get the limited passport from the US Embassy in time and any other documentation needed. However, it would be much better for my business work if I stayed a while longer. If there is an overstay then what documentation is needed?