In the USA, we do use alma mater. Although we use it principally for a college or university, it would not be uncommon to use it for a high school. It would be a little strange (grandiose, perhaps) to use it for a middle or primary school.

I'm not so sure about in the USA, but here, 'Alma mater' would only be used for a University, not a school. We only use 'school' to refer to primary and secondary school, not University. I think that you would only use it for a university that you had graduated from too. We use it a little, but usually only in a formal context. Normally we would say 'my University'.