How can one make up for fasting the past years, and is repentance obligatory if one is unsure about the number of days missed due to exams and studying?

If you are in doubt about your Ramadan fast due to exams, the fast remains an obligation upon you until you make up what you are not certain you fasted and the doubt is removed. If you were ignorant of the ruling concerning what you did, there is no sin upon you if you are among those excused by ignorance, and in this case, you are not required to pay the expiation for delaying the making up of the fast.