Naruto would have a huge impact. His combat skills, like the Rasengan and his ability to use shadow clones effectively, would enhance the team's fighting power. He could also bring a sense of fun and camaraderie that might be different from what the team is used to. Just think about how he'd interact with Obito and Rin, probably making them laugh with his goofy antics.
The story could start with Naruto suddenly finding himself in the past with Team Minato. At first, Minato and the others might be suspicious of him. But Naruto could prove his worth by showing his combat skills. Since he has experience fighting powerful enemies, he could assist Team Minato in their missions more effectively. His presence could also change the relationships within the team. For instance, he might form a special bond with Kakashi, influencing Kakashi's development in a new way.
One interesting plot twist is if they time travel and find that the world they end up in has a different version of the Chakra system. They have to adapt quickly to this new form of energy while also trying to find a way back home. Also, imagine if they time travel and discover that Naruto was supposed to be born in a different village in this alternate timeline. This would completely change the way they view Naruto's destiny and their role in protecting him.
In a Naruto time - travel Minato fanfiction, Minato could be sent to the future. There, he would see how the village has changed, and might be shocked to find out about the Akatsuki and their actions. He could then work with Naruto and the others to fight against the Akatsuki using his unique skills and knowledge of the past. For example, he could teach Naruto some new jutsu that was lost over time.
Time travel can completely change their missions. They might have to redo a mission they already completed in a different way. For example, if they failed a mission in the original timeline, they could go back and try to succeed this time. Or they might have a new mission altogether because of the changes in the timeline that they caused through time travel.
One possible story could be that Team Minato time travels to the future. They would be amazed by the technological advancements. Naruto might be excited to see how the village has grown. They could also learn new jutsu from the future ninjas and take that knowledge back to their own time to strengthen Konoha.
If Minato time - travels, it could change a lot. For instance, if he prevents the Nine - Tails attack, Naruto would grow up in a very different environment. He might not be the underdog he was in the original story. Also, if Minato changes things during the Uchiha clan's situation, Sasuke's story would be completely different. Konoha's political situation would also be altered. There would be less animosity between different clans perhaps.
Obviously, Kakashi is one of the main characters since it's about his time travel. Minato is also a central figure as he is part of Team Minato that Kakashi travels back to be with. And of course, the other members of Team Minato like Obito and Rin are likely to be important characters as well.
It would be very close. Naruto has always longed to know his father, so when he travels back in time to meet Minato, they would quickly bond. They'd probably start training together right away.
A really cool plot might be that Kakashi time travels and discovers a hidden conspiracy in the past that was related to Team Minato. He then has to work with his past comrades, including Minato, to uncover the truth and prevent a great disaster that he knew about from his own time.