The 'Face Stealer' is not based on real events. Usually, such stories are crafted purely from the creative mind of the writer to entertain and engage the readers with fictional scenarios and characters.
He could meet his future self. It would be an interesting encounter as he could learn from his future experiences and wisdom. Or he might meet people who have studied his past adventures and see himself through their eyes.
One interesting story could be that Aang and Katara meet in a different time period, like in a modern world. They have to adapt to new technologies while still maintaining their connection. Aang might be fascinated by things like cars and airplanes, and Katara could be intrigued by modern medicine.
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.
Well, Bell faces the Minotaur at a crucial point in the plot. It's a tense and exciting encounter. But to give you the exact chapter or page, I'd need to refer back to the book myself.
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.
When Yelena meets the Avengers in fanfiction, her interaction depends on the writer's take. She could be standoffish, having been trained in a different way than the Avengers. However, she may also be drawn to their sense of justice. She might start by observing them from a distance. As she gets closer, she could offer her unique skills to help with a mission. Her interactions could range from tense exchanges with the more serious Avengers like Thor, to more light - hearted banter with the likes of Star - Lord if he's part of the group. It's all about how the fanfiction writer wants to develop their relationship.
The timing of the BAU meeting Reid during a case in fanfiction can vary widely. Some might have it happen early on for maximum drama, while others might build up to it later in the story. It all comes down to the author's imagination and plot development.