Is the prayer of one who combines Dhuhr and Asr upon returning from school acceptable, given that he was unable to pray them at their prescribed times because teachers did not allow him to leave to perform them?

You are obligated to perform Dhuhr and Asr prayers within their prescribed times, because studying is not an excuse for combining prayers. The entire earth is a mosque, and you can pray anywhere in the school.

However, if you are unable to pray on time due to the administration's prohibition, then it is permissible for you to combine Dhuhr and Asr by delaying them, while striving to transfer to another school that enables you to perform prayers on time.