Can I apply to Dvision of General Studies and minor music at the same time when I apply to UIUC?
The Division of General Studies is designed to be a no more than at most a two year program from which you then go into one of the colleges for a real major. Though one can minor in music if from another UIUC college, who gets accepted for the minor can be limited (it is definitley not for novices) and is something you cannot declare doing until after you have completed 30 semester hours (one year typically), see https://music.illinois.edu/music-minor, and you should assume you would also have needed to pick some major before doing so.