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).
Literally loved every second of it. Elliot and Margo shine here as they always have in this series. Kind sensitive Elliot is brilliant in this episode.