Not correct. Say eg This is an educational institution, isn't it? eg Is this an educational institution? The standard, literary phrase for such places is
It would depend on the context. The most typical meaning would be a school, most typically, an exclusive private prep school. It could also mean a large library. In the context of the brain, it could mean the cerebral cortex.
For further education, in the UK, I would say college. As slang, young people might say 'Uni' (short for university). In some cases, it can be school (for example, drama school)