There is no neuter (gender-neutral) form of the noun alumnus/a, only masculine and feminine forms. "Alumnus" is an individual male graduate and "alumna" is an individual female graduate. A group of male graduates are "alumni," and a group of female graduates are "alumnae."
For a group of graduates comprised of both men and women (which is what I think the question is attempting to determine), the masculine plural "alumni" is used. Hence, schools have alumni organizations, alumni events, etc.
There is no such word as "alum," although I've seen people use it. The word probably started as someone's misguided effort to employ a gender-neutral term because he was unaware of the applicability of "alumni" to mixed-gender groups.
"Alumnum" is the neuter form of the adjective alumnus ("fostered" or "nurtured"), not the noun alumnus that is the focus of the question above.