Answers to your questions:
1)You will need to apply for an F1 visa to work as a CFI unless you are a USCitizen or have a green card.F1 visa usually allows you to work for an year or two upon completion of the course.After that you will have to leave the US.
2)Yes.Check further with the school
3)Of course.You will need to convert to an FAA CPL/IR and then do your instructors rating.
All the best!
