and after the serie's worst episode, we have what is generally considered as one of the best episodes, as it develops zuko's backstory and gives him a plausible reason for his actions. similairly, we learn more about aang and his past. you already made most of the important points, so i'm not boring you with an anylisys of character motivation.
one thing to point out though. during the scene where aang goes avatar state and saves them, it wasn't that he entomed himself into ice because of the cold water last time, it was his state of mind that made the difference. last time he was alone and afraid, so he reacted by "defending" himself and he subcinciously created a shell to "hide" behind. this time he was much more confident and determined so he faced the challenge head on and pushed through it instead. it shows his growth as a character and his coming to terms with his role in the world. pretty good stuf really.