I read somewhere (meaning I don't know how reliable the surce is) that Rowling once said that most wizzarding families home-school their kids which makes it even more odd because the Malfoys hardly seem like a family who would take ideas for punishment from muggle-schools.
I never thought about that line

I suspect the muggle born, like Hermione, would have gone to regular school, but yes, that is odd.

That never occurred to me and I've read them 3 times!

They do lines at Hogwarts. Professor Umbridge makes Harry do lines in book 5, and Neville mentions the Carrows making people do lines (among other much worse punishments) in book 7.

I thought of Umbridge ... one more reason for her, and the Carrows, to be hated.

There must be governesses or home-schooling, at least for those who can afford it. I wonder how Hermione's parents explained withdrawing her from her ordinary school; Hogwarts must have some cover in place for just such happenings. "We hereby transfer our daughter to the Professor Xavier School for the Gifted; please forward her records to the second stall from the left of the men's lavatory outside Whitehall."

I don't remember which HP book it was, but the one where Harry and his cousin first encounter the dementors, didn't he talk about going to 'normal' school before his 11th birthday?

Oh yes, Harry went to 'normal' school before he was 11 - it's in the first third of Sorcerer's Stone.