If Naruto goes back and his parents are alive, his relationship with them would be a whole new aspect. He would have a family bond that he never had in the original timeline. His father could train him from a young age, and his mother would give him the love and care he always craved. This would also affect how he interacts with others in the village as he now has a different family status.
With his friends like Sakura and Kakashi, things would also change. Naruto might be more confident and less of a prankster as he has the knowledge of the future. Sakura could see a more mature Naruto and their friendship could develop in a new way. Kakashi would also notice the change in Naruto and might start to rely on him more in different situations.
His relationship with Sasuke would be very different. If Naruto stops the Uchiha massacre, Sasuke may not have the intense hatred he had in the original story. They could grow up as friends without the need for Naruto to constantly chase after Sasuke to bring him back.
His relationship with Iruka sensei would be very different. As an old Naruto, he would be more of an equal to Iruka rather than a student. He could share his life experiences and wisdom with Iruka, and they might develop a more peer - like friendship.
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.
His relationship with his former sensei, Iruka, would be really interesting. Naruto could go back and show Iruka how much he has achieved, which would be a really heartwarming moment. And with Kakashi, he could share his experiences as Hokage and maybe even learn some new things from Kakashi in the past.
Well, for Naruto and Sasuke, their relationship might become even stronger earlier. In the past, they could train together more and understand each other's pain from the start. Sakura might be more assertive in her relationship with Sasuke, as she has the knowledge of what will happen in the future. She could try to prevent Sasuke from going down a dark path right from the beginning. And among the other members of Konoha 12, they might form closer bonds as they rely on each other more in this strange new situation of being in the past.
His relationship with his father would be completely different. Instead of growing up without him, he could have a normal father - son relationship. His father could teach him ninjutsu from an early age.
With his friends, he would still be close, but there would be a new level of respect. They would see him as a more experienced and powerful shinobi. For example, Sasuke might have a different kind of rivalry with him, one that is more about mutual growth at the Jounin level rather than just power struggles. Naruto's leadership skills would also be more prominent in group situations, which could change the dynamics of his relationships with his friends.
His relationship with Sasuke might become more complicated. Since Sasuke is an Uchiha and Naruto now has an Uchiha - like power through the transplanted eye, Sasuke could be jealous or feel that Naruto is encroaching on his family's legacy. On the other hand, it could also bring them closer as they now share a similar power source.
His relationship with the Leaf Village would become more personal. He'd be part of the Sarutobi clan in a sense. His bond with Shikamaru and Choji would strengthen as they are Asuma's students. Naruto would also have a new father - figure relationship, which would change how he views authority.
His relationships with his friends would likely be strained at first. They might be jealous of his immortality or worried about how it will change him. For example, Sasuke might see Naruto's immortality as another way that Naruto is 'better' than him, which could lead to more conflict between them. However, over time, his true friends would come to accept it and see it as a way to keep Naruto around forever.
His relationship with Sasuke might change. Sasuke might initially be confused or even critical of Naruto without his headband. But as Naruto shows his determination without it, Sasuke could gain a new respect for him. With his friends like Sakura, they might be more protective of Naruto, fearing that others will target him without the symbol of his ninja status.