What is the ruling on abandoning studies and engaging in exercise, and does exercise then become forbidden (haram)? And what is the ruling on listening to music while exercising, and does exercise then become forbidden (haram)?

There needs to be a detailed explanation of what things are left for the sake of training. If the training leads to missing obligatory duties, such as prayer, then it is not permissible. However, missing permissible things is not forbidden. If studying is a religious obligation, and its time is missed due to training, then it is not permissible to be preoccupied with training over it, for every ignorance that can be dispelled is not an excuse. As for singing accompanied by music, it is not permissible to listen to it. But if it is free of music and of the permissible type, then there is no harm in it.