Dual citizen travelling to China [duplicate]

The US accepts the idea of dual citizenship (sort of reluctantly, but they do). If the immigration official asks on entering the US where you have been, say China. In the event that the immigration officer notices that you don't have a corresponding entry stamp for China in your US passport, you can say you used a different passport.

Yes, your sequence is correct. At least, it's what I do all the time and never had any problems.

1. Always use your US passport to leave and enter the US.
2. Always enter and leave a country on the same passport.
3. Obvious: if you need a visa, make sure you use the passport that has the visa in it.
4. Check in for a flight with the passport that you will use to enter the destination. If your departure country has advanced exit controls, use both passports.
5. If in doubt, ask the airline agent. They actually are pretty good with this. I recently checked in with two passport: using my German one to leave Germany and the US one to enter South Korea. The check in agent wanted to see both for the paperwork.