Aang might become more confident. After the war, he has proven himself as the Avatar and might be more self - assured in his decisions. Katara could become more diplomatic. With the experience of the war and seeing different cultures interact, she may use her skills to help resolve disputes between tribes or nations.
Aang would contribute to the post - war world in fanfiction by teaching the values of the Air Nomads, like non - violence and respect for all life. This would influence the new generation. Katara, being a powerful waterbender, could help with environmental restoration. For example, she could use her waterbending to clean polluted water sources. They would also be involved in diplomatic efforts, as aang's connection to the spirit world and Katara's wisdom would make them great mediators between different groups. Their relationship would also inspire others to work towards a united world.
Their relationship could deepen as they share in the joys and sorrows of rebuilding the world. They've been through a lot during the war, and now they can truly rely on each other. They might become even closer friends at first, with a mutual respect for each other's abilities growing stronger.
In some cases, the anger could be a catalyst for a more romantic development. Aang expressing his strong emotions might make Katara realize the depth of his feelings for her. Or it could be the other way around, Katara's reaction to his anger could make Aang see her in a new light, leading to a shift in their relationship dynamic towards a more romantic one.
They could travel together. Aang, being the Avatar, may still have duties to different parts of the world. Katara, with her skills and their strong bond, would accompany him. They would use this time to not only help the world recover but also strengthen their relationship as they face new challenges and adventures in different lands.
The kids would likely be very kind - hearted like Aang. Aang was always about peace and helping others, so his kids would probably inherit that trait. They might also have Katara's strong will. Katara was never one to back down when she believed in something, and the kids would have that determination too. For example, if there was an injustice in their village, they would be the first to stand up and try to make it right, using both their air and water bending powers.
In fanfiction, they might have a peaceful life. Aang could focus on rebuilding the Air Nomad culture. Katara would be by his side, using her waterbending skills to help the new communities. They could also start a family, passing on their bending knowledge to the next generation.
It could also be that Katara was being overly critical of Aang's progress in learning new skills. Aang might feel frustrated and angry if Katara is constantly pointing out his flaws instead of being more encouraging, especially if he's already trying his best.
One possible storyline could be them traveling the world together to help rebuild the nations. They could use Aang's Avatar powers and Katara's waterbending skills to bring water to drought - stricken areas or help with construction using earthbending - like techniques. Another could be them settling down in the Southern Water Tribe and starting a family while also teaching the next generation about the importance of the four nations' unity.
Their relationship would likely deepen. After the war, they have more time to focus on each other. They'd probably have more romantic moments, like taking walks on the beach or having quiet dinners together. Aang would be more open about his feelings, and Katara would be more affectionate towards him.
You should check out 'Aang and Katara: Love in the Four Nations'. It takes them on a journey across all the four nations, and during this journey, their relationship blossoms. It also gives great insights into the different cultures of the Avatar world and how Aang and Katara interact with them.