All very good questions Cassie. In regards to the women striking against something they're not getting anyway (e.g. sex) even though it appears they are getting it (e.g. Myrhinne), you've pointed out something in the play that thinking actors struggle with. It just doesn't make sense.

The whole premise of Lysistrata's sex strike is a "Happy Idea", meaning it was a well known element of Greek Humor. Thus, it didn't have to make sense. The very idea of women going on a sex strike and taking over the citadel would have been ridiculous to audiences of that day (as ridiculous as greeks fighting greeks was to Aristophanes) and therein would have lay the humor.

I think the important thing to remember when doing this piece of theatre is the style of the piece. Think more cartoon than documentary. I tend to be a thinking actress myself and found myself struggling with this different style in Lysistrata.

http://www.indiana.edu/~thtr/2002/lysistrata/happy_idea.html