It could be that Naruto is trying to prove himself. He wants to show that he can be as great a fighter as his father. Also, he might have received some training or knowledge transfer from someone who knew Minato well. This could have inspired him to adopt Minato's fighting style. He may also be in a situation where his normal fighting style isn't working, so he turns to Minato's as a last resort.
It's really hard to say. Minato is extremely fast with his Flying Raijin and is a very intelligent fighter. But Naruto has an incredible amount of chakra, his Sage Mode, and his Six Paths powers. If Naruto can get close enough to Minato, his brute strength could overpower Minato. However, Minato's speed and strategic mind might keep Naruto at bay.
In some 'minato vs naruto fanfiction', there could be a scenario where they battle in a different dimension. Minato uses his Flying Raijin to quickly move around and Naruto counters with his shadow clones and massive Rasengan attacks. Also, a scenario where they fight not as enemies but in a friendly spar to teach Naruto some secret family jutsu that only Minato knew would be really cool.
One possible reason could be a misunderstanding. Maybe Naruto gets involved in some dangerous situation and they disagree on how to handle it. For example, if Naruto wants to take on a powerful enemy alone but Minato and Kushina think it's too risky.
If the fight got really intense and out of hand, it could also make Naruto feel pressured to choose sides. However, Naruto being Naruto, he would most likely try to find a way to reconcile them instead. This would show his growth as a person and his ability to rise above family disputes.
There are many out there. A really good one might focus on the emotional reactions of Team Minato. For example, Minato might be proud of Naruto's strength and how he overcomes Pain. Kakashi could be in awe at Naruto's new techniques. Their reactions can enhance the overall viewing experience in the fanfiction.
One scenario could be that Naruto underestimates Kiba at first. Kiba and Akamaru launch a surprise attack using their Fang over Fang technique. Naruto is caught off guard but quickly recovers and creates a wall of shadow clones. Another scenario is that Kiba challenges Naruto in a more strategic battle, like in a forest where he can use the environment to his advantage. Naruto, on the other hand, uses his Sage Mode to sense their movements and counterattacks with his Rasengan.
In a Naruto vs Hinata fanfic fight, Naruto has a lot of raw power. He has the Nine - Tails' chakra and a vast array of powerful jutsu like the Rasengan. However, Hinata is no pushover. She has the Byakugan which gives her incredible vision and predictive abilities. If Hinata could get in close, her Gentle Fist techniques could disrupt Naruto's chakra flow. But Naruto's speed and strength might be too much for her. It really depends on the circumstances of the fight in the fanfic, like if Naruto holds back because of his feelings for Hinata or if Hinata has some new power - up.
In a straight - up power comparison, Goku has the ability to reach extremely high power levels that can destroy planets. But Naruto has the power of the Nine - Tailed Fox and his Sage of Six Paths mode which also gives him immense power. If the fight takes place in Naruto's world, Naruto could use the environment to his advantage, like summoning giant toads or using the terrain. On the other hand, if it's in a more open space like in Goku's battles, Goku could use his flight and long - range attacks more effectively. So it's hard to say who would win definitively.
In my opinion, Kirito and Asuna could potentially win. Kirito has his dual - wielding skills and Asuna is no slouch either. They have fought against powerful bosses in SAO. Naruto is strong, but he might be caught off - guard by their speed and teamwork. Kirito and Asuna have a lot of experience fighting together and could coordinate their attacks well. If they can quickly close the distance and take Naruto out before he can use his more powerful ninjutsu, they could be victorious.