Hogy van az alábbi két mondat angolul? Jó úgy, ahogy írtam?

I teach in the XY primary school.

I applied to .... az jó, utána sajnos nem tudom,hogy a major minor dolog mennyire helyes.

a "major minor" that's a contradiction in terms

the word you need is simply "minor"

see 2nd meaning here

[link]

and you teach AT a school unless you mean the building rather than the institution