He would likely become more cautious. After surviving such a near - death experience on the Death Star, he would realize the true power of the Empire and be more careful in his actions against them. His redemption arc could continue as he tries to use his skills for the good of the galaxy, maybe by training new Jedi or helping the Rebellion in secret.
One possible plotline could be Anakin's redemption taking a different turn. Instead of dying, he lives and uses his newfound Light Side strength to help Luke rebuild the Jedi Order. He could become a mentor to the new generation of Jedi, sharing his experiences and knowledge, which is a far cry from his previous role as Darth Vader.
One possible plot could be that Anakin somehow manages to escape the destruction of the Death Star at the last moment. Maybe he uses his strong connection to the Force to find a hidden escape pod or a secret passage. He then has to evade the Empire's search for him while also trying to figure out how to use this second chance to redeem himself further.
Obviously, Anakin himself is the central character. Luke would also be a major figure as he would be interacting with his father in a different way than in the original ending. Leia might also play a significant role, perhaps struggling to accept her father's new existence and having to come to terms with her own connection to the Force through him.
In some fanfics, it could be Anakin's own self - destructive tendencies. He has made so many bad choices in his life that in the end, his own actions lead to his death. For example, if he continues to pursue the dark side without fully understanding its consequences, it could ultimately consume him and lead to his demise.
Anakin can be redeemed in fanfiction by facing his past self. He might have a vision or an encounter where he sees the Jedi he used to be, full of hope and light. This confrontation makes him re - evaluate his choices and strive to return to the path of the Jedi, thus achieving redemption.
Yes, in some fanfictions, Rey is considered as Anakin's reincarnation. This idea often stems from the strong connection to the Force that both characters possess. There are fanfic writers who like to explore the concept of a spiritual or karmic cycle in the Star Wars universe, and this reincarnation theory is part of that exploration.
In such fanfiction, Anakin often makes different choices that lead him to use his powers for good. Maybe he avoids succumbing to the dark side and instead becomes a hero.
If Anakin dies, it would likely change the course of the Clone Wars significantly. The Jedi would lose one of their most powerful warriors. His death could lead to a morale decline among the Jedi and their allies.