What I am asking is: if the word school refers to university as well?
Generally speaking, I think the answer is 'yes' in N.America, and 'No' in Britain.
However, again generally speaking, I think the usual construction is something like 'Harvard is a good school', but not 'Every day after school, the Harvard law students all go to
in Britain, how a uninversity student say: 'I go to school every day'?
When I was in that situation, if I had to describe my day to someone, I'd say things like I go to lectures every day or I study every day or I go to a tutorial every day.
I'm sorry - I got caught up in the last part of your question and forgot about your example. If you are a university student, you would say "I go to the gym every day after class" and "I have classes every day."
I was thinking about "where do you go to school?" or "what school did you go to" as applying to universities as well as other schools. I'm sorry if my hasty answer caused any con