1. As far as Book Three goes, by far the biggest change is that Zuko joins up with the Gaang in Book Two during “The Chase”, so he is already a well established member of the Gaang, the same way Toph is, since they joined at about the same time. In part this means that when they sneak on board the Fire Nation ship and sail to the Fire Nation, he is there to share in the despair and fear they’re all feeling. He is also able to smooth over some bits of Fire Nation culture clash for them, like explaining to Aang that the clothes he picked are a school uniform, and if he wears them, he’ll get dragged in for truancy.
2. Hama takes one look at the former Fire Nation soldier traveling with the Avatar and his friends and singles him out for kidnap. He goes missing under the light of the full moon, and the gaang sets out to find him while Katara studies waterbending with Hama. Afterwards, Hama’s story, and Hama’s rearrest, bring up Zuko’s past as a prison guard. He opens up to the Gaang about the Boiling Rock and his experiences there.
3. On the Day of Black Sun, Zuko tells the Gaang how to get into the bunker, but other than that, not much changes. Azula is still able to delay them for long enough for the eclipse to end, and they still have to escape by the skin of their teeth, leaving the adults behind.
4. Speaking of the Boiling Rock… Zuko’s story means that Sokka knows where his father and the other Southern Water Tribe warriors are probably being kept. He takes Zuko with him to get them. At the Boiling Rock, things have changed since Zuko was there last. Mai’s uncle has been transferred away, and Mai herself is a prisoner, in a cell next to Suki’s actually, because that’s just the way Azula is. Also at least half the guards know and recognize Zuko, and it’s not hard for him to spin a yarn about being transferred back. It’s Sokka who gets caught and thrown into prison, and it’s his presence as one of the Avatar’s companions that causes Azula to come, only to find her brother there too, leading an escape. In the end, Sokka and Zuko are able to rescue their girlfriends and Sokka’s dad, and it’s Ty Lee who fights to protect them and is thrown into prison for her betrayal.
5. After the Boiing Rock, when Azula attacks, the Gaang flies off and accidentally finds the Sun Warriors. Aang and Zuko have their little dance with the dragons, Sokka makes fun of them, the Sun Warriors glare at him, Katara hits him in the head. Good times.