What's your interpretation of this situation? What could he be thinking?

I would definitely say that he likes you and is flirting with you. All of the things you listed, even the ones that you think don't mean anything, say to me that he is flirting with you in his own way, and doing it when his friends aren't around so he won't get made fun of. Him telling you another girl is pretty is probably just him trying to make you a bit jealous or make you think he doesn't like you, which is also evident in the way that he ignores you some days. He's probably trying to come across as liking you but doesn't want to make it obvious. If you like him, go for it. Good luck!