Visa F suites my situation?

I am a student, with US citizenship, and currently studying in University of Gothenburg in Sweden. I will go to China as part of a project. The project is a collaboration between my current project supervisor/professor in Sweden and a professor in Chinese Academy of Science in Beijing. However, I am NOT admitted to the Chinese Academy of Science in Beijing. The duration is expect to around a month.

1. Someone suggests that I apply for F type. Is that the right choice?
2. I'm currently in Sweden, with US passport. I suppose I still submit my application to China Embassy in Sweden?
3. Am I allow to visit nearby countries, like Japan or Taiwan, for a few days, then re-enter China with F?

Thank you.