>>Not sure if this is what you'd meant by lack of education, but when do Hogwarts students learn English and Math and History and other things that they do seem to know, but never had in school?<<

That's part of it, but the author of the fanfic also pointed out how Hogwarts students don't learn Latin, even though that's what the spells are cast in (mostly), a lot of theory and science behind many subjects are left out, and many types of magic are very narrow in scope or left out all together (e.g. Defence against the dark arts and Animagi transformations).

>>Or do they figure they learned enough of that stuff in primary school before they got to Hogwarts... but except for Harry and other Muggle-raised, when/where do they go to primary school.<<

Yes, I believe primary school is the assumption for muggle-raised students, and I believe tutors are implied for the magical raised students.