Jean-Paul Sartre was a French philosopher who explored the meaning of existence through his writings, otherwise known as existentialism. Margo's mention of him may allude more specifically to his play No Exit (1954), about condemned souls confined to a room together for eternity.
Breaking the moon in half would not cause its fragments to fall: the moon is in orbit around Earth, and therefore so are the fragments. They would just start to spread out very slowly around the orbit (which is 800 times larger than the moon).
Hale Appleman's acting is just brilliant! It's so hurtful to see him struggling and trying to ovary up as Margo would say, but at the same time so hopeful because we all know how good he is.
A kind reminder to not fear to open up and face the unknown.
I guess some burdens are just meant to be shared.