Goku might run into past versions of his friends. He could see a younger Krillin or Bulma and have some really interesting interactions. He could also meet past versions of his enemies and try to change their fates. For instance, he could meet a young Vegeta and try to steer him away from the path of evil. This would be a huge change in the Saiyan's story.
In the fanfic, Goku could become friends with Naruto easily. Since they both have a strong sense of justice and a will to protect their friends. Goku might teach Naruto some of his training methods, like training under heavy gravity. And Naruto could show Goku the unique aspects of ninja villages and how they function.
Well, he could change a lot of things. Maybe he'd prevent some of the big battles or save some characters who died. For example, he might stop Frieza from destroying Planet Vegeta earlier. It would be a whole new timeline with different outcomes.
Another thing that could occur is that he might accidentally create new threats. By interfering with the past, he could disrupt the natural flow of events and cause new villains to emerge or existing ones to become more powerful in different ways. It's a risky move going back in time, even in fanfiction.
When GT Goku goes back in time in fanfiction, his character may change in many ways. He could be more of a planner, thinking ahead about how to avoid the mistakes of his original timeline. He might also be more protective of his friends and family, knowing what they had to endure in the future. His sense of responsibility would likely grow, as he now has the power to shape the past and create a better future. This could lead to him being more involved in the political and social aspects of the Saiyan and Earth communities, rather than just focusing on his own training and battles.
Well, Vegeta would be a likely character. He might be initially suspicious of the female Goku. Maybe he thinks she's a threat or just can't believe there's another Goku - like being. He could be there to add some comical moments as he tries to understand the situation.
In general, it's a bit of a toss-up. The strength of Manga Goku and Anime Goku can vary depending on the specific arcs and battles. Sometimes, it might seem like one is stronger in a particular situation, but that could change in another.