"The music volume is too loud and might disturb the others."
It is fine, but 可能会 is the more acceptable answer since here it means that it would disturb others, but more gently than it could be e.g. by replacing 会 with 以免、否则会……
Yes, it can, but for reasons I just stated "might" might be a better answer.
It sounds smoother with it but is fine without.
These exercises are so inconsistent. There is another exercise in this section that says something like "Turn down the music volume..." and it doesn't use 的，and so when I leave it out in this exercise it gets marked wrong. These inconsistencies are really confusing and aggravating.