How do I deal with the "Music Education" core course at the institute, and is it permissible to listen to classical music that is free of dubious elements, knowing that I regularly recite the Quran and pray?

Music is forbidden by scholarly consensus, and there is no difference between its types. It is not permissible to study music as a subject except out of necessity, provided that it is impossible to continue permissible studies without it, while attempting to avoid it or minimize it as much as possible.