Using "put hair on your chest" for women
The answer to Part 1 of your question is It depends
It depends on:
-
The age of the woman to whom you are speaking (don't, if she is over 25)
Your age relative to her age (should be about the same, and it is OK if you are obviously senile)
The sense of humor of the woman (it should be earthy and robust)
How much you care about your relationship with the woman (if you care, be careful)
Whether there are other people around (If she feels she has to fake being a good sport, you are dead)
Never say anything like that if you are in a position to influence her career.
There is nothing to be gained by such a remark, and much to be lost. It is not a mere extension of addressing a group of men and women as "you guys".
Think of the reverse: How would it strike you if a woman told a chubby man that he should wear a bra? (Not an exact analogy, but close enough.)
The movie "Willow" had Val Kilmer use this expression in reference to the young princess. So in short yes it can be used as in there is no codified prohibition against it. You can also use it literally, for example a woman about to begin gender reassignment, the doctor could tell her the hormone therapy will put hair on her chest. As an aside I think to use the plural "hairs" is uncessary as "hair" is a mass noun.
I think it means it will give me the feeling of discomfort and unfamiliarity and the momentary delusion of feeling like a full-grown chest-beating growling man, and I would be able to strut my feathers like a peacock, the stuff being in lieu of having actual feathers on your chest. And be the focus of envy for weeks to come. Regardless if you actually wished for hair on your chest.
Like the Camel or Marlborough advertised feeling.