I'm not sure how much it will matter in the end because the academies I'm interested in teaching at all consist of degreed teachers, so not sure they are going to be interested in someone who doesn't have (or currently pursuing) a music degree.
Regarding your schedule, I would recommend being up front about your availability. Find days and times that you will be able to consistently be available and offer those times. Some music schools want a commitment of at least, say, 8 hours per week. If you can't do that, they might be willing to have you as an overflow teacher (e.g., for 1 or 2 students who they can't fit in otherwise) or as a substitute.Or you can look for another music school that better fits your availability.