One idea could be that Kakashi travels back to the moment right before Obito's 'death'. He uses his knowledge of future events to prevent the cave from collapsing on Obito. Then, together they are able to rescue Rin more effectively and change the whole tragic course of events.
Their relationships would become much stronger. Kakashi would no longer have to bear the guilt of Obito's 'death' and Rin's loss. Obito would be extremely grateful to Kakashi for saving his life and would likely view him as an even greater friend and ally. Rin would also be happy to have both of them by her side, and they could form a very tight - knit team.
Kakashi is known for his laid - back yet highly skilled nature. His influence on Naruto could be in terms of teaching him to be more strategic in battles. Rin, being kind - hearted and having a strong sense of care, would give Naruto the emotional support he lacks. So Naruto might become more balanced in his approach to life and ninja - hood.
One great Kakashi and Minato fanfiction is 'The Legacy of a Teacher'. It beautifully portrays Minato's influence on Kakashi. Another is 'Mentor and Student's Bond'. It delves deep into their relationship during Kakashi's early days. And 'Minato's Unfinished Business' is also a good read, showing how Minato's spirit might guide Kakashi in later challenges.
Yes, there might be. The Naruto fandom is quite large and diverse, so it's possible that someone has written a fanfic exploring the idea of Kakashi and Rin as Sakura's parents. You can try searching on popular fanfic websites like Fanfiction.net or Archive of Our Own.
In a fanfiction of Kakashi and Rin's love story, it could start with their time in the ninja academy. Rin was always drawn to Kakashi's natural talent and mysterious aura. Kakashi, on the other hand, was initially oblivious to Rin's feelings. One day, Rin got injured during a training session. Kakashi carried her all the way to the medical tent. That was the first time he realized how much she meant to him. As they grew older, their bond deepened, and they found themselves falling in love while on various missions.
The fanfiction 'Minato's Last Words to Kakashi' is extremely emotional. It focuses on Minato's final moments and the words he leaves for Kakashi, which are full of love and hope. Another one is 'Kakashi's Regrets about Minato'. It shows Kakashi's inner turmoil over things he wishes he could have done differently with Minato.
Some Minato and Little Kakashi fanfictions might focus on the political and social environment of the Hidden Leaf Village at that time. How did this environment affect their relationship? For instance, the village's expectations of its ninja, the power dynamics among different clans, and how Minato and Kakashi navigated through these aspects. It could also be about how their relationship was perceived by others in the village. Maybe some were jealous of Kakashi for having such a great sensei, or perhaps they saw the potential in their partnership for the future of the village.
In a fanfiction, Kakashi and Minato could be on a mission together in a dangerous, unknown territory. There could be traps everywhere. Minato, being the faster one, might rush ahead to scout but accidentally trigger a trap that causes some damage to him. Then, when Kakashi tries to help, he might also get injured by the after - effects of the trap or other hidden threats in the area.