I've looked at the first half of your question here:
In various parts of western Europe, beards on men went in and out of fashion throughout the Middle Ages and early modern era. The only constant I can think of that might compare to the emphasis on women's smooth legs/underarms is that a hairless face is an essential part of male beauty through the connection with youthfulness. (This is distinct from the association between manliness and beards that occurs from time to time.) Christine de Pisan, who is possibly the only Christian woman to describe the physical characteristics of a man identified as "beautiful" in the Middle Ages, refers to his beardless chin. A few religious women writers I can think of who describe Christ in their visions as beautiful say little more than that he is youthful.
(I'm focusing on women writers here because the tradition of pederasty, with an adult man and a younger teenager or boy, still holds some sway in the medieval Mediterranean world--either in actuality, or as a literary topos. So men describing other men as "beautiful" has a different cultural meaning.)