If Gohan travels back in time, his relationship with his father, Goku, would be really interesting. He could train with Goku as an equal, which would be a different dynamic from their usual father - son - student - teacher relationship. Goku would probably be surprised but also excited to have such a strong partner to train with.
His powers would likely shock the past characters. They might see him as a great hope or a potential threat. If he uses his powers openly, it could change the way the Z - fighters train and view their own power limits.
It could strengthen his relationships. If Gohan has the gamer ability, he might be able to use it to protect his friends and family better. This would make them trust him more and bring them closer together. For example, he could quickly analyze a dangerous situation using his gamer skills and save his loved ones, making his relationships deeper.
His relationship with his friends could change significantly. For example, if he travels back to a time when they were younger, he might be more protective of them. He could also inspire them in different ways, leading to stronger bonds. His relationship with his sensei might also be affected. He might be able to offer new insights based on his future experiences.
If Noctis traveled back in time, his relationship with Luna could be drastically different. He might be able to save her earlier or have more time to develop their relationship without the impending doom hanging over them. Their interactions could become more tender and less rushed.
Some students might be afraid of him. His sudden outburst of anger could make him seem intimidating. So, they would keep their distance from him.
In time travel fanfiction, if Jiraiya goes back, it can have a huge impact on his relationships. He may be able to save some relationships that were lost in the original timeline. For instance, he could repair his broken friendship with Orochimaru. Regarding his relationship with Naruto, if he travels back to Naruto's childhood, he can be a more effective teacher and friend. This could lead to Naruto trusting him even more. And if they travel back together, they rely on each other more in the different time period, which enhances their bond.
Well, if Gohan starts acting like Vegeta, it might strain his relationship with Piccolo at first. Piccolo is used to the more mild - mannered Gohan. But over time, Piccolo might come to respect this new assertive side of Gohan. With his father Goku, Gohan's new Vegeta - like behavior could create some friendly rivalry. Goku might be a bit surprised but also excited to see this new side of his son.
If Spider - Man travels back in time, it could strengthen his relationship with Uncle Ben. He might get a chance to really talk to him and understand his values better, which would in turn make him a better hero in his own time. Also, his relationships with his friends like Ned and MJ could be affected. For example, if he changes something in the past, he might come back to a different present where their relationships have shifted.
In a time - travel scenario, Anakin's relationship with his mother could be greatly altered. He could go back in time and save her from the Tusken Raiders. This would change his whole outlook on life and his path towards the dark side. Regarding his relationship with Palpatine, he would be aware of Palpatine's true nature from the start. So, he could either avoid Palpatine completely or try to expose him earlier. His relationship with other Jedi, like Ahsoka, could also be different. He could be a better teacher and mentor to her, as he has the experience of his future mistakes.
If Kakashi travels back in time, his relationship with his father would be completely different. Instead of the strained relationship due to his father's perceived failure, he could support his father and build a strong bond. With his students, if he travels to the future and then back, he might have a new perspective on how to train them. He could be more lenient or more strict depending on what he saw in the future of their development.