Translation:The tall teacher is not English, but Hungarian.
Google Translate suggests that a translation of "Englishman" would be the literal "angol férfi." I think "angol" in this context is an adjective, not a noun like "Englishman," which is also part of why it might not work.
Right on that. But please note that Hungarian does not make that distinction between the noun and adjective forms with nationalities. So, both "he is English" and "he is an Englishman" translate to "(ő) angol". If you want to emphasize the noun role, you can add "egy" - "a", as in "My English teacher is an (actual/real) Englishman" - "Az angoltanárom egy (igazi) angol". But that is totally optional.
The usage here feels closer to the adjective role but, since there is no real distinction, maybe the noun version should also be accepted.
This have the same meaning as the. As far as we don't have context. So, I think this should be also acceptable.
the teacher = a tanár
that teacher = az a tanár (=that is the teacher)
this teacher = ez a tanár (=this is the teacher)
You should preferably put quotes around your words.
"This" and "the". Makes it so much easier to read it.
How odd. Sometimes Magyar is ok to translate as "Magyar," but not in this sentence? Duo insists on "Hungarian:" All the "Hungarians" I know (including my grandma) say they are "Magyar".
The Hungarians say they are Magyar, but the English call them "Hungarian". We're doing English translations here. :)
The word "Magyar" is also used in English when referring to Hungarians, especially when talking about the early Medieval Era. I think "Magyar" should be an accepted translation too, even if the word "Hungarian" is used more often.