Traveling from China to Vietnam

Hello, I am traveling from Toronto to Beijing and then Nanning to Hanoi. I am a US citizen and I read that the flight to and from China has to be originating from and returning to the US. Is this the case? Also do I am from NY with an NY drivers license, but I live in DC. Do I have to apply at the NY office as that is where my consulate region is or can I apply at the DC office?