How come in this case the verb can be left out but it can't always be left out when the verb is "to be"? What are the rules about that?
In the present tense "to be" is ommitted in third person singular and third person plural, except when you mean "there is/are". In other tenses and person it can't be ommitted.
If you wanted to say 'she is a man now' how would this be said? I gather that there is no way of differentiating between he and she.
correct, there's no direct way of saying "he" or "she" in Hungarian. You need to understand that from the context. "She is a man now" -> Ő most egy férfi. That could very well refer to a man who was a boy yesterday but became a man overnight and now he is a man. If you want to be specific then you must use "girl" or "woman" in the sentence, like "Ez a nő most már férfi" -> This woman is now a man. The word "már" indicates that she has become and man and will be man in the future as well, i.e. the change is permanent.