Anakin is the central figure, of course. The Jawas might be more involved as Anakin could interact with them more often if he stays. He might also meet some new characters, like a hermit living in the Dune Sea who has ancient knowledge about the Force. And the local merchants in Mos Eisley could have more interactions with Anakin, as he might be involved in local trade or helping them deal with pirates or other threats.
Obviously, Anakin would be the main character. His mother, Shmi, would also play a significant role. There could be his friends from the pod - racing days like Kitster. And perhaps some Tusken Raiders who might have a different relationship with Anakin since he stays on Tatooine. Maybe they would see him as a more permanent threat or, in an interesting turn, a potential ally in some local matters.
In this fanfic, Anakin could stay on Tatooine because he has a premonition of the dark side that awaits him if he leaves. So, he decides to stay and focus on bettering his home planet. He might use his natural piloting skills to start a small trading business, using his pod - racer as a start - up vehicle. This would keep him occupied and away from the events that lead him to the dark side in the original story.
His mother, Shmi, would definitely be a main character. She could play an even more important role in Anakin's life, guiding him in using his abilities for the good of Tatooine. Also, Watto, the junk dealer, could be a significant character. Their relationship might evolve from one of slave - owner and slave to something more complex, like a grudging friendship or a business partnership as Anakin grows older and more skilled.
The Hutts would likely oppose Anakin. They have long held power on Tatooine through illegal and immoral means, and Anakin's takeover would threaten their control over the planet's criminal underworld and trade routes.
In the 'anakin never left tatooine fanfic', it could be that Anakin, staying on Tatooine, discovers ancient Force secrets hidden on the planet. These secrets could be related to an old Jedi or Sith presence long forgotten. He might use this knowledge to better the lives of the people on Tatooine. For example, he could use these newfound powers to improve the farming techniques or build better shelters. His story would be one of a local hero, using the Force for the good of his home planet rather than for galactic domination or the fight between the Jedi and Sith.
Obviously, Darth Vader and Luke Skywalker are the main characters. Vader is the one on the hunt, and Luke is the target of his search.
Well, perhaps Anakin would start by reforming the podracing scene. Since he was once a podracer himself, he could make it safer and more fair. He might also train a new generation of pilots. And he could use his influence to improve the living conditions of the slaves on Tatooine, maybe even free them all. This would completely change the social structure of the planet.
Padmé Amidala could also be a part of it. Since she has a strong relationship with Anakin, she might notice the changes in him due to the training. She could either support or be worried about the new Anakin that is emerging under Mace Windu's tutelage. Additionally, some of the other Jedi Council members like Plo Koon or Ki - Adi - Mundi could be involved, perhaps observing Anakin's progress and having their own opinions on it.
Anakin's mother, Shmi, would likely be a very important character. Since Anakin is not being trained as a Jedi, he would be more focused on his family. Shmi's influence on Anakin would be even greater, and she could play a role in guiding his actions and decisions, especially in relation to the local community on Tatooine.
I haven't read this specific 'Never Left Tatooine' fanfic in detail. But generally, an analysis could start with the plot. Maybe it focuses on a character who is stuck on Tatooine and how their life unfolds there. It could explore the local cultures, the unique landscapes, and the relationships the character forms within the Tatooine setting.
Obviously, Anakin is a crucial character. The slaves themselves would also be important. There could be a young slave boy or girl who Anakin befriends and who serves as a symbol of hope for the others. And the slave masters, as the antagonists, are important too.