In Twelfth Night, what does Viola learn about herself regarding her feminine and masculine sides?How does acting as a man complete her feminine side?

There a two specific ways in which "playing" a man gives
Viola insight into herself.

The first is that, by playing
the part of Cesario, she is able to have access to Orsino that she would be denied as a
woman.  Shakespeare lived and worked in a time when especially high born men and women
had to follow many strict rules about spending time together.  Spending time alone
together would have, generally, not been possible for an unmarried man and woman.  So,
Viola, as Cesario, is given the rare chance to simply "hang out" with Orsino and have a
regular, "man to man" chat with him.  This access allows her to develop real feelings
for a man she has come to know, rather than rely on love from a more superficial
distance.

Secondly, her interactions with Olivia allow her
to stand outside the female experience and witness it as an observer.  By witnessing
Olivia's love for her, she can experience, albeit secondhand, a woman's expressing her
love to the man she desires.  Viola, constrained by her disguise, cannot tell Orsino of
her love, so it is possible that she sees and understands her own womanly feelings
better through her interactions with Olivia.