Why isn't "egy" required here before "ügyvédet"?
Some Hungarian sentences can remove "filler words" because the context of the sentence and meaning are still intact without them
Shouldn't the translation be: Péter does not see a lawyer.
Yes,that's a reasonable translation, and I'd say report it if the question comes up for you again.
That is now the preferred translation.
How does it come, that the same sentence can be singular and plural? Lawyer and lawyers are shown correct here. No distinction at all in hungarian?
In Hungarian, the sentence is definitely singular, but one could say Peter does not see a lawyer, Peter does not see any lawyers, or even Peter sees no lawyers, and they all mean the same thing.
Is it only for lawyers, or for nurses, teachers, animals a.s.o. as well?
There is nothing special about lawyers here. All these words in Hungarian have plural form that differs from the singular.
Is it just me or is ‘Péter’ stress-initial? It really confused me.
Aren't Hungarian words stressed on the first syllable as a rule? Why would Péter be an exception? Or do you hear a stress on the last syllable?
You make a distinction and take the plural form of e.g. lawyer only if you await several lawyers. If the question is a general one, you leave the noun in the singular form.
Why was "the lawyer" marked as wrong?
Because "the lawyer" implies a definite lawyer but the Hungarian sentence has no definite article in it.
A couple centuries ago "Péter sees not any lawyer" would have been the preferred English.