When Kim Jong Ill is singing about how lonely he is, it's logical to assume it's because he's a tyrant whom no one loves or likes. However, considering that he's actually an alien cockroach sent to conquer the Earth, it makes perfect sense: he's singing about there's no one like him on the planet, and thus, is completely alone.
The song "Pearl Harbor Sucked" plays before Gary returns to the team. Since he's a great actor, he would have a love song bashing a crappy romantic drama running through his head. In fact, he's the one singing it.
At first, it seems odd that all the members of Team America (Save for Spotswood and INTELLIGENCE) are 20-something year olds that simply were top graduates (or a football player) from state colleges. None of them are from Ivy League Schools or had done anything truly remarkable before joining Team America. However, it makes perfect sense when you think of America: It's the American Dream to go from a (relative) no one to someone who's rich and well known by the world. That's what happened to all of the Team America members, they went from nobodies to rich, famous militia men and spies who the world knows (though mainly despises).