"Are you a lawyer?"
Because you focus the verb itself which pretty much kills a copula sentence (ie a sentence where you assign concepts to each other, like in this case, "you" and "lawyer"). Sounds like "Do you exist (as) a lawyer?"
I'm having some trouble with this one, I've tried both "Ön vagy ügyvéd" and "Te vagy ügyvéd". Is the vagy assumed?
Ön is the formal "you" and the verb that goes with it is "van". It's third person singular and therefore "van" is omitted. The conjugation is correct in your other sentence but you should put "vagy" at the end. "Te ügyvéd vagy"
Vowel length... Again. Wrote "Őn űgyved?" for "Ön ügyvéd?" Sometimes accented short vowels seem long to me. Probably my ears need more time to get used to Hungarian phonetics.
You omit the verb only in 3rd person (but then you must) - see what hatcher said above:
Én ügyvéd vagyok? Te ügyvéd vagy? Ő ügyvéd? Ön ügyvéd?
Mi ügyvédek vagyunk? Ti ügyvédek vagytok? Ők ügyvédek? Önök ügyvédek?
In the first approximation, nothing. In the second approximation, which is perhaps not part of any language course of around A1-B1 levels, I would say 'Ügyvéd vagy-e?' adds a certain flavour to this question which keeps the conversation at a colloquial / friendly / more informal / lower level. 'Ügyvéd vagy?' is colloquial alright, but, to me it is dry, formal, cold, empty. I would imagine that the addressee of this inquiry would almost reach for his/her certificate to prove that he/she is indeed a lawyer. As a matter of course, it is difficult to build any context from short questions like these. Just my $0.02.
'Maga' is a personal pronoun for 3rd person singular (the plural form is 'maguk'). It is formal, but not as formal, as 'Ön/Önök'. There happens to be yet another, old personal pronoun: 'kend', of which plural is 'kendtek'. These are not very formal, but rather somewhat pejorative. E.g. 'Ügyvéd kend?' (I suggest that you do not try it in the lawyer's office.)
'Vagy ügyvéd?' is not correct. 'Ügyvéd vagy?' is.
'Maga/Ön ügyvéd?' and 'Ügyvéd maga/Ön?' are all correct.
You never use 'vagy' in 3rd person, so the correct answer should be: ön ügyvéd?