The first example is okay. It's more likely that people might say "He eats too much." because that is more informal than "He has a big appetite." and therefore is more like the first sentence, "No wonder he's so fat." Fat" is a word that's possibly offensive, but it's often used by two people who are gossiping about a third person (who can't hear the conversation). A more neutral word is "overweight". The second example needs to be "I can't make it because an emergency has come up."