Maybe Zuko has his own goals that don't involve chasing Aang. He could be more focused on redeeming himself in other ways, like helping the Fire Nation people or learning about different cultures without the need to pursue Aang.
One idea could be a time - travel fanfiction. Zuko and Aang could be sent back in time to the era before the war started. They would then have to use their knowledge of the future to prevent the war from ever happening. This would involve them working together to change the minds of key people and stop the events that led to the conflict.
There is some. Some of them might explore their relationship in the context of the Avatar universe's adventures, while others could be more about their personal growth and how their relationship develops over time. It really depends on what kind of story you're interested in.
One great 'Aang and Katara and Zuko' fanfiction is 'The Fire and Water Alliance'. It delves into how they work together to rebuild the world after the war. Their different abilities and personalities create interesting dynamics.
One common theme is friendship. Since they start off as enemies, many fanfictions focus on how they build a strong bond of friendship. Another is redemption. Zuko's journey of redemption is often explored further in relation to Aang.
I'm not sure specifically as there could be many different stories within that fanfiction. It might be about Zuko and Aang's relationship, perhaps in an alternate universe or a situation not shown in the original series. It could explore their friendship, their adventures together, or even some creative scenarios that fans have come up with.
One memorable moment could be when Zuko defends Aang against a group of Fire Nation soldiers who still see Aang as an enemy. Zuko stands in front of Aang and uses his firebending to protect him, showing that he has truly changed sides. Another moment might be when Aang helps Zuko face his inner demons by using his Avatar state to enter Zuko's mind and give him the strength to overcome his past traumas.
Well, in a zuko x aang fanfic, the exploration of their powers together can be really interesting. Aang can control air, water, earth and fire, and Zuko is a firebender. Their combined abilities can create unique storylines, like fighting a new enemy that requires both their skills. Also, their friendship has so much potential for development in fanfics. They start from being on opposite sides and then gradually come to understand and care for each other, which can be explored in many different and fascinating ways.