Cram till late at night is pretty normal for most East Asian country IMO.
Vietnamese here, used to have to go to the teacher's house to do cram study until 9 or 10.
"The only thing that doesn't feel realistic in this series is Azumi's godlike speed."
Not the unbendable or unbreakable blade? So far Ichigeki is the only manga in which they actually teach people to throw away sword and replace it with fallen enemy's.
She is not a samurai, not even a sword...