"I am the musician."
Translation:Én vagyok a zenész.
Is the "En" obligatory in this sentence? Is it emphatic, like I am the musician, not somebody else?
No it's not, I live in Hungary and they say both variants. And I don't understand why Zenész vagyok is wrong.
"Zenész vagyok" is "I am a musician" - that is what I am is a musician. (Question: what are you?) "Én vagyok a zenész." is "I am the musician" - it isn't him or her it's me (Question: who is the musician?)
The English is an answer to the second question - "Who is the musician?".
Yes, it is emphatic, though -- as the English sentence can't express the same emphasis in writing, without context -- it doesn't necessarily have to be. "A zenész vagyok" would also be correct. (Though there are probably less possible contexts where that could be said.)
"Zenész vagyok" without a determinate article would be translated back as "I am a musician".
That is the verb, otherwise the entire sentence makes no sense. It's the "I am" part of the sentence. What could be dropped is "én", by saying, "A zenész vagyok". This looses the focus from me being the musician that is in the original translation. Depending on context one or the other would be more appropriate.
There are a lot of sentences where the copula is omitted. Ez egy asztal. Ő férfi. So your explanation is at best incomplete.
Only third person of the verb lenni (van/vannak) is dropped in some situations. First and second person must always include the verb. There are a number of threads that go into this in more detail.
I used "zenésznő", but it wasn't accepted. Is there something wrong with the sentence "A zenésznő vagyok."?
Maybe it was not accepted because you didn't use én ? That is also not obligatory but apparently duolingo wants én to be in the sentence
van is used for third person (he or she) - but in this sort of sentence it must be dropped.
"The musician is me" is very bad English! The correct English is "I am the musician" - Én vagyok a zenész.