About Order lands:
We know that even poor people like Elt and Primera can enter the Order's military academies if they have some talent.
There are academies of magic and sciences, some attached to the Order military, like the Magitec institute in Lescatie, which train heroes to fight, while others, like Saint Welsple Academy teach geography, natural history, and elementalism, and even poor people like Mimiru and Saphirette Spherica can enroll.
The fact that Mimiru and Saphirette could enroll in good academic institutions despite being poor as rats, implies that there are free or at least affordable primary and secondary schools in Order lands. I don't think Saphirette could graduate at 16 years old after only two years of study unless she had a good previous foundation. And somebody had to teach Mimiru the basic spells when she was 5.
About Mamono Friendly lands:
The Wandering Scholar mentions that they are less developed than Order lands, and that they are magnets for adventurers and ruffians.
I guess there are some schools and other academic institutions, but they are probably fewer in number and worse in quality to those from Order lands.
Domesticated Mamono and their husbands probably send their daughters there so they can integrate into human society and so they can start seeking future husbands. Many Mamono marry very young, so they probably stop studing early.
About Zipangu and the Mist Continent:
The situation is probably similar to feudal Japan and Imperial China. Most peasants would be illiterate, but there would be schools in the cities, and education would be valued. Mamono probably study side by side with human children in many places in Zipangu.
About Demon Realms:
Only Mamono are born there, and they all know that they will have to leave their homeland and go to human lands to seduce or hunt a husband. Their education and training probably is mostly about survival in human lands and stuff that will help them get men.
Mamono can survive only on sex, food is grown with barely any effort, many Mamono produce valuable substances with their own body, and their husbands probably will come already trained in useful crafts, so learning how to support themselves isn't a top priority when compared to getting a man.
The Sabbath is probably a very important educational institution. The Mamono send their girls there, and the Sabbath can teach not only sex stuff, but also magic.
Many Mamonos have their own traditions. The Inari have their own schools, and the Crow Tengu are scholars who train their young in magic. The Dwarves and Dark Elves probably keep their old education systems running.
The Royal Makai is very big and has a lot of different Mamonos and Incubi from all around the world, so there may be some decent schools besides the Sabbath, but on the other hand, everybody is extra horny in the Royal Makai, so the average Mamono probably focus on sex more than usual.
And you have the wild Mamono who live in the forests and mountains, hunting, gathering and looting. Those will learn their survival skills from their parents.