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.
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?
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.
I struggle with question intonations in Hungarian. To me they rarely sound questioning. Any tips?
Try to look for other resources outside Duolingo
with the new TTS voice, questions do not sound like questions, at all.
Thank you. I would welcome any suggestions for other resources.
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?".