What did it mean to be a woman in Shakespeare's time and place? What concepts and ideas regarding gender do you think he held? How do you see his views differing, perhaps, from that of his society?

The age in which Shakespeare began his writing career was the Elizabethan age, named after the unmarried female monarch who ruled England at the time, Queen Elizabeth I. There is no doubt that her reign raised questions about whether women were fit to be in charge, but she led England in a time of relative peace and prosperity and is still considered a great leader. But even with an unmarried woman occupying the highest social position in the land, women in Shakespeare's age were still limited. Women had few freedoms in regard to marriage and property ownership, and they were also not allowed to act on stage. There were many expectations governing their everyday lives.
For this reason, all the female parts in Shakespeare's plays were played by men dressed as women. And even though females themselves were limited in that they could not act, the female characters Shakespeare created show no such limits. From Lady Macbeth's calculated ambition to Juliet's teenage love affair, the women in Shakespeare's plays live robust lives. They come from various classes, cultures, and spheres of influence. Some are happy, some are unhappy. Shakespeare does not paint all women as the same, and he gives some of his female characters roles that are often moving, comical, tragic, and even empowering.
https://history.hanover.edu/hhr/00/hhr00_2.html