Why not: Are you the teacher?
There is no "the" (a, az) in the Hungarian sentence.
Is the indefinite article the norm when not stated otherwise?
Are you the teacher?= Őn a tanár?; Are you (a) teacher?= Őn tanár?
can it be like "Tanar vagy?"
It can, but it's informal. You'd ask that from someone with whom you're on a first name basis.
Duo, please allow sound-on (to listen) to pronunciation AFTER the question is already answered!
If asking it could mean is he or her a teacher.
That would be "Ő tanár?"
Ön is only used as formal you.
Is it always capitalised?
Not capitalising ön and önök can be seen as a sign of disrespect, but it's not incorrect grammatically.
I think it is the new fashion to capitalize "Ön", "Te", and derived words. There is no grammatical base for this, as far as I know.
It IS incorrect! As vvsey said, it's just a new fashion.
It's definitely accepted to capitalise second person pronouns in formal documents to show respect. See here.
New fashion ≠ incorrect
"Ms" as a title wasn't very popular until the 20th century, but now it is unmistakably a correct form.
Surely 'You're a teacher?' also correct?
Ön is supposed to be formal, so imagine asking this question to a stranger or to someone whom you want to impress or show respect to. A better translation of "You're a teacher?" would be "Tanár vagy?".