Is it really wrong to add a 'vannak' at the end of this sentence?
Yes, it is absolutely wrong. It is not optional, it is wrong in this case.
Mi zenészek vagyunk.
Ti zenészek vagytok.
In some places it seems ok to use van/vannak, but in other places it is wrong. How do you distinguish between them?
Use van/vannak when describing where something is or when using an adverb (e.g. "She is fine" - Jól van).
Do not use van/vannak when describing what something is (Az egy könyv "that is a book") or what its attributes are (A könyv piros "the book is red").
Very helpful, thank you!
OK - now I understand it too!
If they are lányok, shouldn't they be zenésznők?
There is no such word in Hungarian. Only a few professions/occupations make that distinction. It is basically irrelevant in this case, so there is no separate word.
Mizinamo, thank you. That explanation is clear and so helpful. Köszönöm szépen