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.
Minato's time travel could have a huge impact on the power balance in the Naruto universe. If he travels back and teaches some of his techniques to other ninjas earlier, it could change the way battles are fought. He could also influence the development of new jutsus. And if he goes to the future and brings back knowledge, Konoha could become far more advanced than other villages. This would shift the geopolitical situation among the ninja villages. His presence in different time periods could also inspire new generations of ninjas in different ways.
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.
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.
Well, at first it would be very strange. Minato would be confused by this female version of his son. But as they interact more, if fem Naruto shows her familiar Naruto - like spirit, Minato would start to see her as family. He might become very protective of her in the past world, which is different from their normal father - son relationship.
Their relationship would likely become more equal. In the original story, Minato was more of a distant, heroic figure to Naruto. But through time travel, they can interact as peers, sharing knowledge and experiences. This would deepen their bond.
One possibility is that Naruto's presence in the past would disrupt the timeline significantly. However, it could also lead to a strengthening of Konoha. He and Minato could work together to improve Konoha's defenses and train the next generation of ninjas earlier. This could potentially change the entire future of the ninja world, making it a more peaceful place with Naruto's knowledge from the future.
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.
Jiraiya is likely to be a popular character. He was Minato's teacher and has a strong influence on Naruto as well. In a time travel fanfiction, he could provide a lot of wisdom and help in the different situations they encounter. Also, Tsunade could be important. Her leadership skills and medical ninjutsu could be very useful when they are in the past, and she has her own history with both Minato and Naruto's family.
Emotionally, Naruto would become more confident and stable. Having his father back would fill a void in his heart. This new - found emotional strength could translate into better chakra control and more powerful jutsu. Minato could also guide Naruto in handling the power of the Nine - Tails more effectively.
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 great 'Minato x Naruto Time Travel Fanfiction' is 'A Father's Chance'. In this fic, Minato travels back in time to Naruto's childhood and gets to be the father he always wanted to be. It's really heartwarming to see their interactions.