1. If you mean the final results for all of the classes you have taken, I would use the word 'transcript'. If you just mean the results of one exam, I would use 'exam result'. Another common term, mostly used for grades received in elementary and secondary schools, is 'report card'.
(Transcript: an official report supplied by a school on the record of an individual student, listing subjects studied, grades received, etc.- from dictionary.com)
2. I am not sure if this has a specific name, but you can always use the terms 'proof of enrollment' or 'official schedule', depending on the situation.
3. 'Diploma' is the correct word.
Another note: You are talking about pieces of paper, as opposed to peaces of paper.
Student or Learner