Well, without wanting to do the whole exercise for you.... ;)
The important point is that the PP in (1) is an adjunct, while that in (2) would naturally be taken as a complement - i.e. "student" is a relational noun, you have to be a student of something*. I think this should enable you to sort the rest of the assignment out.
* As one linguist I know might put it, to be a student you need an argument :).
Student or Learner