Edward might meet his parents. Since he has the chance to go back in time, he could meet them when they were alive and perhaps learn more about alchemy from them, which could change his future actions.
In this kind of fanfiction, Edward might try to change the past events that led to his and his brother's misfortunes. Maybe he'd prevent the failed human transmutation in the first place, saving Alphonse from losing his body.
Alphonse Elric is often present. He might play a role in helping Edward understand and use his new gamer - like abilities in relation to alchemy. For example, he could be the one who discovers a new aspect of Edward's powers.
Well, perhaps Edward could use his alchemy skills in the magical world of Hogwarts. He might be sorted into Gryffindor for his courage. He could start to learn magic along with the Hogwarts curriculum and have some interesting interactions with the students like Harry, Hermione and Ron. Maybe he'd show them some unique alchemy tricks and in turn learn some new spells.
Yes, there are likely fanfictions out there with such a concept. The worlds of Naruto and Fullmetal Alchemist, where Edward Elric comes from, are quite different, but that's what makes the idea of a crossover in fanfiction so interesting. Writers might explore how Naruto's ninja world and its unique powers could interact with Edward's alchemical abilities and the complex world of Amestris.
In fanfiction, the possibilities are nearly endless. Regarding Edward Elric becoming a homunculus, it could be a very interesting concept. If he were to become one, it would completely change his relationship with other characters. For example, his brother Alphonse might react in a very different way. Also, Edward's own view of himself and his abilities would be transformed. His struggle with his new form, if it were to happen, could be a central theme in the fanfiction. Maybe he would try to find a way to reverse the process, or perhaps he would embrace his new existence as a homunculus. It all depends on the creativity of the fanfiction author.
Edward's intelligence. He is a brilliant alchemist. A fanfic could explore how he shares his knowledge with the reader, perhaps teaching the reader alchemy. This could lead to some really interesting adventures where they use alchemy to solve problems in their world. And the reader could also bring out a different side of Edward as he gets closer to someone who is not as experienced in alchemy as he is.
They could start by comparing their different worlds. Edward would explain about the principles of alchemy like equivalent exchange, while Urahara would talk about the Soul Society and the way spiritual power works. This exchange of knowledge could be the foundation for their relationship in the fanfiction.
Perhaps it's a story where Naruto has the same kind of tragic backstory as Edward. Maybe Naruto loses Sasuke in a way similar to how Edward lost his mother and brother's body. So Naruto starts to study alchemy in the hope of getting Sasuke back. Along the way, he meets Edward and they learn from each other's experiences and fighting styles, and together they face the challenges in both their worlds.
Obviously, Edward Elric himself is a very popular character. He's the protagonist of the original story and his return is the central theme, so he's always in the spotlight in these fanfictions.
One likely character could be a rival alchemist who is jealous of Edward's skills and reputation. Another might be a villain from the original story who has a grudge against Edward. Also, a new character created specifically for the fanfiction, like a power - hungry alchemist who thinks Edward can help him achieve his goals.