Is it permissible to listen to a committed song with music once a year in an educational context? And is it valid to pray Dhuhr and Asr combined or as a make-up prayer outside their prescribed times due to work necessity?

Listening to music and musical instruments is undoubtedly forbidden, so it is not permissible for you or the students to listen to anything that contains music, as there is no necessity that calls for it, and there is no obedience to a creature in disobeying the Creator.