Is it gramatically correct to call my classmate in a unibersity a unibersity coleague? Or is the term coleague used only for professional staff workers.
Grammarly, yes. Semantically, I would say no, cause the first impression of the phrase to me is that you work, instead of studying, in the university and so does your mate. You can use "schoolmate" to describe it. "Colleague" is mostly used to describe someone who works in the same business or field.