The first sentence, "Ne yersin, ne icersin," does not mean «Que manges tu, que bois tu.» - It's an idiomatic expression that means something like "What's up?" "What's happening?" - a colloquial expression for "How are you?"
Yes, of course those are the literal meanings of "ne içersin" and "ne yersin" when they are each seen alone, but the complete phrase "Ne yersin, ne içersin" is an idiomatic expression.