Do former NAHL players who were just cut by USHL teams have to go back to the NAHL team they played for last year? Or, are they free agents? Does it depend on whether the NAHL team kept them on the protected list?

Yes I believe it depends on whether someone stayed on the protected list.

If they released them they can go wherever they want

If they never released him they own his rights and he has to play their or request a trade