1.1
He wonders why Aang is so kind to him. For his part, he cannot imagine being so unthinkingly and persistently friendly to someone who hunted him across the world, someone who tried to have him killed. He's curious about where a person can even find the energy to be both so gregarious and so forgiving. He finds himself hoping that it is not particular to the ways of Aang's people and, thus, doomed to be lost in breadth of a lifetime.
1.2
He thinks that wondering why Aang is kind to him is an irrelevant and pointless consideration that he shouldn't actually devote thought to at all. His singular focus is and should always be teaching firebending in order to help restore balance to the world. Regardless, he still comes back around to the thought that Aang really is a nice kid.
2.
He thinks of Mai in inappropriate ways. He pictures her stripped naked, pale, slim, and beautiful. Her eyes are inviting and her petal-soft mouth has the faintest trace of a smile. He remembers the taste of her and the way that her hair slides through his fingers. He thinks about doing...things. Some that he already has and others that he, regrettably, didn't get a chance to try.
3.
He thinks that Sokka is a decent enough guy. He reviews all the annoying things that the other boy has done since the last time he thought about it and figures that they were mostly teasing. Zuko remembers very limited experiences with good-natured teasing throughout his life and decides that his tolerance level is on the rise. He tries to figure out jokes Sokka has told that he didn't get before dismissing them as Sokka's failures and not his own.
4.
He doesn't think about his father and sister. Not for long, sad moments where he feels deprived and wonders if he'll ever really experience how families are supposed to be. Not at all.
5.1
He wishes that Toph would stop going through his things. He feels mildly guilty about it, but is glad that she's blind, nonetheless. She cannot read the private things he's written down that he'll probably never even show to those to whom they are addressed. The letters to Mai, particularly, he is sure, would garner him ceaseless ridicule. He certainly doesn't want to give her more nickname fodder.
5.2
He also wishes that Toph would use fewer nicknames in general. It just makes it all the more difficult for him to keep everyone's actual names straight.
6.
He scoffs internally at Haru's mustache (and sometimes forgets the internal part). He does not think, but rather knows that mustaches are stupid and nothing of which to be so excessively proud. The fact that Sokka claims to be able to grow one in a day only further proves his point. (Not that Zuko believes him.)
7.
He wonders if Katara will try to make good on her threat. He usually decides that she won't, but only out of respect for Aang's wishes. He wonders if her insults will remain as pointed, her glares as heated, or if it will all eventually fade into complacency. He leans towards pessimism. He thinks that this is his burden as the scion of the Fire Nation. This is the truth that he told his father. This is his penance.
8.
He wonders where his Uncle Iroh is. He fears that Uncle will be so angry and disappointed with him for taking so long to understand that he won't forgive him, that he won't care anymore. He does his best to dismiss those thoughts and remember that Iroh is not and will never be Ozai.
9.
He thinks of Mai some more. He remembers her laughter, a smokey chuckle, and the way she crinkles her nose when she's annoyed. He hopes that he doesn't die before he gets the chance to hear or see those things again. (Then he thinks about what else he hopes to see again and his mind wanders back to thoughts of her naked.)
10.
He wonders where his mother is, but immediately stops himself. He knows that he has no idea where to start looking. The fate of the world is on the line, so he also has no time to be selfish. This seems only to guarantee that he thinks about it for even longer.