I am finishing a master program with a J-1 visa with two year rule and sponsored by my government. Now I got accepted to a PhD program in the US with a fellowship that covers tuiton and pays stipend. However, according to the school, I need to apply for F-1 in order to receive the award. I asked the officers of my sponsor whether I can apply for F-1 and they said no. My government will let me to have PhD too but will not be sponsoring it anymore, according to our agreement. However I am confused about which visa I need. My questions are:
1- Can I legally apply for F-1, when I go back to my country in this summer?
2- If I can apply, do I really need a written permisson from my government? Will I have a problem in the US Embassy about this situation?
3- Is this true that I will be obligated with two year rule even when I have the F-1 visa?
4- I know many schools let their students to be J-1 and still give them fellowships. My school says they can never pay me stipend without F-1? Why do you think I am having this problem?
5- Which visa is better when I want to find a job in the US as a professor?
Thank you so much for your help, I reall appreaciate your knowledge and hardwork.