Air Leak/Snorting at the back of nose while playing clarinet?

The "snorting" problem that you started with after the audition sounds like it's a failure of the muscles that seal off the nasal passages while you're blowing through your mouth into the clarinet.

1. Why does air come out of my nose when I play clarinet?

Why does air come out of my nose when I play clarinet?

In a normally-functioning pharynx, the soft palate remains firmly sealed when blowing through the mouth. In SVPI, the soft palate is unable to seal firmly enough, or to maintain the seal throughout the exhalation. This allows air to escape into the nose.