1) "Party pooper" is a slang expression which means somebody who brings down the mood, somebody whose presence stops others from having fun. It is something you don't want to be. The joke is interpreting that expression literally. 2) Okay, I think this one is really funny! The phrase "write on an empty stomach" is ambiguous. To do something "on an empty stomach" means to do something while very hungry. But "to write on an empty stomach" could also mean to put your pen on somebody's empty stomach and write something. If you're going to write on something, you should write on paper. :)

A "party pooper" is basically someone who ruins the mood of a party, making it less fun for everyone involved. The first joke is basically just taking it literally, as if it meant "someone who poops at parties." Frankly, it's not very funny. "On an empty stomach" is a common phrase. It just means "while hungry". For example: "You shouldn't take your final exam on an empty stomach" means you should eat something before the test. This joke is also deliberately misinterpreting the idiom by treating it like any other prepositional phrase.