No. Fanfiction that involves sexual content about characters is not appropriate. These are fictional characters often aimed at a wide range of audiences, including younger viewers. Such fanfiction goes against the family - friendly nature of the original works and can also be considered disrespectful to the creators' intentions.
They could embark on a quest to find a lost relic. Aang's airbending skills and Katara's waterbending would be crucial in overcoming the obstacles like ancient traps and dangerous creatures. Their teamwork would strengthen their bond.
One great fanfiction idea could be them sharing a picnic by a beautiful waterfall. They could talk about their dreams and how far they've come together. This would be a really sweet and innocent moment that shows their deep connection.
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.
Katara could be heartbroken. She might initially be in denial, not believing that Aang has actually left. Then she could become angry, feeling betrayed by Aang's sudden departure.
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.
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.
In some fanfictions, it might be part of a plot to create tension. The writer wants to show that their relationship isn't all smooth sailing. So, Katara hurting Aang can be a device to make the story more interesting. It could also be related to different character arcs, like Katara trying to become more independent and in the process, her actions accidentally harm Aang.