I have a question about the word order. Normally I thought that nem comes before the verb. Does using hanem make a difference or is this order always possible?
I don't think so. Hungarian has (almost) free word order (with some rules and stuff), so it depends more on what you want to emphasize. Here the importance is on the word angol: "I'm not English, but Hungarian." The emphasis goes with whatever is right before the conjugated verb. Being at the start of the sentence is secondary.
In English, we sometimes put the predicate before the subject, for emphasis. "English I am not!" Or even, stiffly and archly, "English I am most certainly not, my good man!" But it works, I suspect, only when the subject is a pronoun. Let me try:
--Hungarian I am! ("I" = subject.) --A man you are. ("You" = subject.)
Now I'll try a noun as a subject:
--The drill is the tool. ("Drill" = subject.)
--The tool the drill is. ("Drill" is perhaps supposed to = subject, but the sentence word order sure confuses that.)
It looks like the OSV (Hungarian I am) way of saying might come from Celtic. A more Germanic, V2 way to emphasise it would be "Hungarian am I" (OVS). Like in the Spongebob Squarepants theme: "Absorbent and yellow and porous is he".
Either way, both structures are falling out of use and could just confuse/irritate people if one were the preferred translation.
I was wondering because once I said "Nem éhes vagyok," but I was corrected to "Nem vagyok éhes"
You can say 'Nem éhes vagyok' and either continue the sentence with what you really are or not - in the latter case it will be implied that you are something else than hungry. Thirsty, tired, in love, whatever.
It is not compulsory to use it. In case you do use it, there is a slight stress on it - as if there would be someone else around to be English, and you would like to make sure you are certainly not one.
i am Canadian and Hungarian, in hungarian you use the word "hanem" but in english you would not use the phrase "i am not up, but down"
Proper names of persons, and geographical entities, institutions, that's basically it. Names of days and months are not capitalized, nor are the names of peoples.
There are some inconsistencies though, as in other languages. The name of the celestial body is Sun/Nap, still in Hungarian it is written 'A nap süt.' (The sun is shining). Same thing with Moon/Hold and Föld/Earth.
it doesn't accept "I'm English..." as the correct answer, the suggested answer is "I'm not in English (!)"
Horrible indeed - sorry for that and thank you. Currently Duo accepts the following:
I am not English, [I'm/I am/but] Hungarian. I am not English rather Hungarian. [I'm/I am] not [/an Englishman/English] but [I am/I'm/] [/rather] [Hungarian/Magyar].