At first, it would create a sense of shock and confusion within the team. Sasuke might seem less interested on the surface but secretly be worried. Sakura would be visibly distraught. Kakashi would have to deal with the immediate chaos of trying to find Naruto and also keeping the remaining team members in line. Without Naruto, the team's balance is thrown off. Naruto was often the source of energy and motivation in the group, so his absence could lead to a more somber and less enthusiastic atmosphere in Team 7.
He might first find a place to hide, like an abandoned building. There, he starts to realize how difficult it is to be on his own. He has to find food and water by himself.
In a Naruto fanfic where Naruto runs away from Kushina, it could be due to various reasons. Maybe he feels misunderstood. For example, Kushina might be too strict with him in the fanfic's storyline, not allowing him to pursue his own ninja way freely, so he decides to run away to find his own path and prove himself.
One idea could be a crossover where Ben 10's Omnitrix malfunctions near Avatar Aang's world. Ben and Aang team up to face a new threat that is causing chaos in both their realms. Maybe some of Ben's alien forms have unexpected interactions with the bending abilities in the Avatar world.
In a fanfiction, the Avatar State of Aang could be used in a more creative way. For example, Aang accidentally enters the Avatar State during a cultural festival. His friends are initially worried, but then they realize that in this state, Aang can communicate with the spirits present at the festival in a unique way. He learns secrets about the spirits and their connection to the human world, which he then uses to strengthen the bond between the two realms when he's out of the Avatar State.
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.
Perhaps Naruto feels that Kushina is being overprotective. He wants to prove his independence and go on his own adventures without her constant supervision, so he decides to run away.
He might miss out on some crucial training. Jiraiya has a lot of knowledge and skills to pass on, and by running away, Naruto could fall behind in his development as a ninja.
One possible reason could be that Naruto might be afraid of the intense training Jiraiya has in store for him. Jiraiya is known for his strict and grueling training methods, and Naruto, being young and sometimes impatient, might just want to escape that for a while.
One great Aang fanfic could be one where he has to face an unexpected new threat in the Spirit World. It might explore his growth as the Avatar even further, showing his unique connection to the spirits and how he uses airbending in creative ways to overcome challenges.