Men are considered smarter than women in today's society, which connects to the idea in this excerpt that it is unthinkable for women to have Shakespeare's genius.
Gatsby did not leave West Egg even though Nick tells him to do so because he was waiting for Daisy to give him a call and a go-signal that both of them will run away and live a different and brand new life together. Gatsby was a hopeless romantic that was just waiting and has always been waiting and wanting for the love of his life, which was none other than, Daisy.
It is for if you die, or get seriously injured then it simply says that it is not the places fault but it is your own. Places usually do it to avoid being sued.