Can a professor copyright an exam?
As far as the material being redistributed... It will be redistributed solely for educational purposes, i.e. emailed to a friend or student taking the class in the future to help them study and prepare for an exam.
(I do know that redistributing an exam will tend to upset professors, and many professors recycle exams, however, that is another issue. My concern here is strict legalities and whether I can or cannot redistribute an exam under fair use for educational purposes.)