His relationship with Jack Harkness would be particularly interesting. If he goes back far enough, he might meet a younger Jack. This could change their dynamic completely. Maybe he would see Jack in a different light, or Jack might see Ianto as a mysterious figure from the future. Their relationship could develop in a whole new way, either strengthening their bond in a different timeline or creating a rift between them depending on how things play out.
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.
In the past, Ianto might also have relationships with people outside of Torchwood. He could fall in love with someone in the past, which would make his return to his own time very difficult. He would have to choose between the life he had in the past and the one he left behind, including his friends and his duties at Torchwood.
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.
One possible plot could be Ianto Jones going back in time to prevent a major disaster in Torchwood's history. Maybe he travels back to the time before the Cardiff Rift opened in such a large and dangerous way. He could use his knowledge from the future to stop an alien invasion that was the root cause of the rift's instability.
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.