Is magic taught in schools, alongside other classical subjects like PE, chemistry, languages (if schools in Y'ren work like they do here on earth)? Is it taught to kids at a very young age or is there a legal boundary to it?
(really enjoying the lore dumps lately <3)
(really enjoying dumping the lore lately! <3)
Though these answers might be a bit more vague than you expected.
Schooling does work similarly to Earth - the accessibility of proper education is highly dependent on the country you live in, the size of the community you live in, and sometimes your financial situation. Most of my characters live in a country called L'yeshkao, so my answers will be in that context. L'yeshkao is a well-developed nation: It has a few very large cities, many big towns, and also some very rural villages, tribal lands, and wilds roamed by nomadic groups (tl;dr ymmv a lot with education). Most of my characters live in the capital, so I'll focus on that-
But I'll answer your second question first!
Byondi do not have magic when they are very young. They are born in a 'natural form' with their soul in an inert state (presumably coiled in the chest - at least, according to many byondi mythologies). A byondi's soul emerges into its auric form when they're around 9-12 years old. That's the first moment you would know their elemental alignment, the first time they can access magic, and when they'll achieve a 'common' form (their natural form, but with slight appearance changes due to influences from the soul - hints of their beast form, basically). It is like a spiritual puberty, haha.
Very young byondi are not taught about magic in schools but in the home, they will be exposed to it and will learn proper manners, both cultural and practical (no beast form in the house, etc.).
Newly realized byondi will be taught about magic in school as soon as possible. They'll join a PE-like class focused on teaching the practical, quality-of-life aspects of magics. Students will learn about its everyday uses and how to properly execute ordinary abilities that all byondi have (how to transform, don't teleport into a solid object, etc.). There might be magic extracurriculars for upperclassmen in grade school but no student combat is allowed.
From a higher learning perspective, byondi in large cities have the most options. You could learn magic (from a theoretical/intellectual perspective) as an academic/scholar from the same types of institutions that would teach other higher learning maths, sciences, etc. You could also learn magic as part of pursuing a profession, typically via a trade school or apprenticeship. Or, you could learn magic as a hobby/club for combat sports. Byondi love combat - it's a way for them to blow off steam, practice their craft, and display their prowess. It's very common, especially for city byondi, to be engaged in combat sports or spectate them frequently.
Rural byondi have fewer options. Smaller populations tend to be more homogeneous (single-element) and education is often focused around practical use (e.g. a town of Earth byondi that relies on trading ore will focus on teaching its youth skills relevant to mining). It's common to have to move away to a city if you want to learn something new/different. Despite that, these populations are generally very magically adept because their livelihoods depend on it. I would say the average rural byondi is more magically adept than the average city byondi, but the skill ceiling is much higher in the city.
You could also just not learn magic! Not using magic can be an indicator of high social status, implying you are so well off that you do not need to perform labor or defend yourself. Wearing clothing that is not conducive to a winged form is an indicator of high social status for the same reason.
(It varies culturally of course. a Light who doesn't learn magic is perceived as worthless and an embarrassing failure because Light society is elitist and wealthy).