He might start by observing. Aang is a curious person, so he'd likely watch how people live, how they interact with technology. He may also try to find other benders to learn about any new developments in bending. And he'd probably use his kind heart to make friends easily in this new future environment.
Aang might go into a deep state of depression. He has always been an emotional character, and having his heart broken by Katara, someone he loves deeply, could send him into a downward spiral. He might isolate himself from his friends and stop practicing his bending for a while.
Well, Aang being the Avatar has a deep connection with the elements. In this fanfiction, perhaps he enters the Avatar State and uses all his elemental powers in harmony. He could use waterbending to create moisture and cool the volcano, combined with his airbending to disperse the heat and gases.
Aang could save the Airbenders in the fanfiction by first finding out the root of the threat they are facing. If it's a powerful enemy bent on destroying them, he may seek allies among the other benders, like the Earth Kingdom or the Water Tribes. He'd then use his airbending to scout the enemy's territory undetected. Once he has all the information, he could use his skills to either directly confront the enemy or find a way to neutralize the threat. For instance, if the enemy is using some sort of dark magic, Aang could use his pure Avatar energy to dispel it and free the captured Airbenders. And of course, he'd use his airbending to fly around and quickly transport the Airbenders to a secure location.
His refusal can also build tension. Other characters might not understand his stance, or they might be frustrated by it. This can create conflict within the story, both between Aang and his allies, and between Aang and his enemies who might not expect his mercy. For example, some of his friends might think that killing a particularly dangerous enemy is the only way to ensure safety, but Aang stands firm, causing a rift in their relationships. This adds an extra layer of drama to the plot.
Naruto's experience in handling loss and grief can be of great value to Aang. Both have lost important people in their lives. Naruto can show Aang how to turn that pain into strength. By sharing his own journey of dealing with the death of his loved ones and still moving forward, Naruto can help Aang not be consumed by his own losses and instead use them to fuel his growth as the Avatar.
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.
Well, physically, a female Aang might have different hairstyles and clothing. Instead of Aang's simple monk robes, she could have a more feminine take on them, like with added ribbons or a different cut. Her hair could be longer and styled in ways that are more typical of female characters in the Avatar world. In terms of her bending style, it might be more graceful. While Aang was fluid, a female Aang could bring an extra level of elegance to her airbending moves.