What is the ruling on making up missed prayers for more than a year, and is it obligatory to interrupt one's studies (school and university) to make them up, and how should they be made up, whether continuously or intermittently?

If you violated these conditions out of ignorance, there is a difference of opinion regarding the obligation to re-perform these prayers whose conditions you partially violated. You are permitted to follow those who do not deem re-performance obligatory. However, if you wish to re-perform them, you are not required to leave school or university. Rather, you should re-perform them according to your ability, in a way that does not harm your interests or studies. If you were to re-perform them for two days each day, that would be good.