Well, when Merlin travels back in time, his relationship with his mother would be quite different. He might be able to spend more time with her and learn more about his heritage. His bond with Gaius would also be altered. In the past, Gaius might be more of a mentor figure than he already was, and Merlin could learn new things from him. Regarding his relationship with the magical creatures, he could form stronger alliances with them in the past, which would give him more power and resources in his new timeline. This would in turn affect how he interacts with the non - magical humans as he would have more leverage.
His relationship with Morgana would be a complex one. In the past, she might not be as corrupted as she later becomes. Merlin could try to befriend her and prevent her from turning to the dark side. This would change their relationship dynamics completely. With Uther, Merlin would have to be extremely careful as Uther hates magic. He might have to hide his true self more than he did in his original time, which would strain their already difficult relationship. Also, his relationship with the druids could be enhanced as he could have more time to learn from them and help them in the past.
If Merlin travels back in time, his relationship with Arthur would be very different. In the past, Arthur might not trust him at all at first. Merlin would have to prove himself all over again. With Gwen, he might be more aware of her future importance and try to protect her in a different way. And his relationship with the other knights could be completely new, as they might see him as a stranger with strange powers.
If Ianto travels back in time, his relationships with the Torchwood team in his original time would be put on hold. They would be left wondering where he went. In the past, he might form new relationships. For example, he could become friends with an ancestor of one of his present - day colleagues. This would create a strange connection between the past and the present for the team when he eventually returns.
His relationship with his father Poseidon would be different. He might see a side of Poseidon that he never knew before, like when Poseidon was younger and less experienced. This could change how Percy views his father and their connection.
If Natsu goes back in time, his relationships would be very different. With his friends, he might have a new level of understanding. For example, he could see how they grew up and the challenges they faced in the past. He might be more protective of them, especially if he knows what's going to happen in the future. His relationship with Lucy could also change. He could see her in a new light, perhaps realizing things about her that he didn't before when he first met her in the present.
If Goku travels back in time as a Super Saiyan in fanfiction, his relationship with his past self would be complex. His past self might look up to him as a hero and a mentor, but at the same time, there could be some envy or confusion. With his Saiyan comrades, he could become a leader figure much earlier, changing the power dynamics among them. Also, his interactions with Earthlings would be different. They would be more fearful or more in need of his protection, depending on how he uses his power in the past.
If Bilbo goes back in time to when he first met the dwarves, his relationship with them would be quite different. He would already know them well, and they might be more suspicious of his prior knowledge. But he could also use this to his advantage and form even stronger bonds with them more quickly, as he would understand their personalities better from the start.
His relationship with Kakashi would also change. Naruto could use his Rinnegan - enhanced knowledge to help Kakashi deal with his past traumas earlier. He might also show Kakashi new jutsu or ways of combat that he learned in the future. This would make Kakashi see Naruto in a whole new light and their bond could become more of a teacher - student relationship in reverse.
With his Slytherin peers, Draco's relationship would shift. He might encourage them to be more inclusive and less focused on pure - blood supremacy. This could make him an outcast among some of the more traditional Slytherins, but also gain him new allies who are open to change.
His relationship with his father, Ned Stark, would be different. He could finally have a real father - son relationship instead of the hidden one. He might be able to learn from Ned and become an even better leader in the North.
His relationship with Katara would be very different. He might be able to approach her in a more confident way, knowing what they've been through in the future. He could also avoid some of the misunderstandings that happened between them in the original timeline.
His relationship with Sasuke would be very different. In the new dimension, Sasuke might not have the same vendetta against his brother. So Naruto wouldn't have to worry about Sasuke going off the rails. With Sakura, she could be a powerful ninja in a different way, like she might be more focused on medical ninjutsu and Naruto would see her in a new light. And his relationship with Kakashi could change too. Maybe Kakashi is a strict military - like leader in the other dimension instead of a laid - back teacher.