>OTOH we can have an "International" school, where students from all over the globe study.

Well, my daughters would qualify to be the first international students, as they've all studied a bit at home before coming here and are nationally mixed already. But there's no way that each student in such a school would be international.

>Imagine if you had similarly an "inter-racial" student, in a school that accepted people from all races. Would that student have to be of mixed blood?

I'd call that mix a tincture.