F Visa 01 Entries

Similar question from my side: I got a F 30 days visa with which I entered China 2 weeks ago. A Chinese visa agency informed me that they can give me a 3 months extension.
1. Does that mean that I can stay for 3 months from the day on they issued the visa?
2. They can only issue single entry visa, but they said that this would allow me to leave the country once and enter again (as stated above, my visa says 01 Entries). Is it correct or can't I leave once and come back within this month?

Thanks in advance