"She is our neighbor."
Translation:Ela é nossa vizinha.
Yes, it is correct.
Articles are optional when placed before possessive adjective pronouns.
But bear in mind that Portuguese people often use the article while Brazilians not at every time. Anyway, using it or not in this kind of sentence is grammatically correct.
I wrote "for men" or general sense, not that for "women" it should also be "vizinho". Just refer to my answer below.
I keep getting this problem, where a group of people of unknown gender is given the feminine gender. In this case if she was the neighbour of a group of guys who were sharing a house would it not be 'Ela e nosso vizinho'?
no, vizinho has to agree with the word it's being referred to, so use vizinha,