I just re-read your post. Whether you can audition to multiple degree programs at the same university depends on the school. It varies, and it’s a little hard to find the people who can accurately answer that question sometimes! My son was able to do it at the schools he applied to, and in some cases got acceptances on two instruments and to both music Ed and performance at the same school. It complicated the application process and the awarding of scholarships at some schools (they really wanted to know what he planned to study before awarding music scholarship money at half his acceptances and one of the others just awarded money based on his strongest audition I think).
Music Ed audition is usually the same as a performance major with the addition of an interview for music Ed.