1. What does 'You are the man!' truly mean?
You the man! or
you da man is used as an idiom what the Cambridge dictionary says is correct. If you are intending on using the idiom, leave out the
The Cambridge Dictionary puts it well, but is perhaps a bit too general:
used to praise a person who has done something well
The word praise is too general in my opinion. This idiom is used often to congratulate or thank someone someone for being skilled or doing something well immediately after they have done it.
What does it truly mean? It's all down to context and how it's used. In some cases it might be used to congratulate or thank someone for their excellence, or to express more general praise. I think the most important part of the phrase is the definite article 'the'. It is saying that:
You THE man
As distinct from all the other men. Some might say that it is similar or the same as saying:
You are the first or best of all men.
2/3. Can it be used for a woman, can we say 'she is the man'?
In my opinion, no, because it is a gender specific idiom. Using it in reference to a woman may suggest that a woman can only be the best if she is a man. Women may find that offensive.