I'll answer anyway, even if I don't specifically speak American or British (or Australian ;) English, although my English is slightly more British-based.
(a) I would use either points or marks. I don't think anyone uses 'scores grades'.
(b) exams and tests are different. Exams are more important/formal. You do an exam at the end of a course. You might do a test during the course, and it would not score as highly as an exam, if at all.
(c) grades and scores are different. Scores are marks out of some total, e.g. 15 out of 20, or 75%. Grades are normalised scores on a limited range, e.g. A-E (with our without +/-) or 1-5.
Your final one is fine.