Both majors train teachers, so you can choose either one as a middle school teacher. Discipline teaching is a master, and curriculum and teaching theory are masters.
3. The two majors are different in nature and have a long academic system. Online search has the introduction of masters and masters. It is relatively possible to apply for the subject teaching (physics or mathematics) major.
4. It is suggested to go to official website to check the professional catalogue and other information. I don't know about information purchase and remedial classes.