Maybe Kakashi could be the one. He's always been Naruto's mentor in many ways. He has the knowledge and skills to train Naruto for such an unusual task. He could use his Sharingan to analyze the fanfiction and teach Naruto how to spot the dangerous elements within it.
Well, perhaps Naruto is forced into a strange situation where he has to combat the ideas and stories in fanfiction that are causing some sort of chaos in the ninja world. Maybe some evil force is using fanfiction to distort the real story of the ninja world and Naruto is the only one who can stop it by 'killing' these false narratives.
Well, Naruto would probably gain some really unique magical abilities. Fairy Tail mages are known for their diverse magic, and Naruto could combine his chakra skills with something like Fire Magic or Celestial Magic. He might become even more powerful in combat, with new ways to attack and defend.
Naruto would gain better combat awareness. Kurama's experience in battles can be passed on to Naruto. He'll be able to read his opponents better, know when to attack and when to defend. This will make him a more formidable opponent in combat situations.
Yes, there are likely to be such fanfictions out there. The idea of Naruto being trained by Ichigo combines two very popular anime characters from different series. Fanfiction writers often come up with creative crossovers like this. You can try searching on major fanfiction platforms to find specific works.
One possibility in this fanfiction could be that Naruto gains new and unique combat skills. Monkey D. Dragon is known for his revolutionary ideas and powerful abilities in the 'One Piece' world. Under his training, Naruto might learn different ways of strategizing and approaching battles, perhaps incorporating some of the more unorthodox fighting styles from the 'One Piece' universe. This could lead to Naruto becoming even more formidable, not just in terms of his ninjutsu, but also in his ability to lead and inspire others in a different way, much like how Dragon has an impact on the 'One Piece' world.
Maybe Muu is a long - lost member of a powerful clan that has some special connection to Naruto's Uzumaki heritage. So he takes it upon himself to train Naruto to help him reach his full potential and also to preserve some ancient techniques or secrets related to their clans.
I'm not sure who the specific author of that fanfiction is. There are so many fanfiction writers out there that it's difficult to determine without more research.
It could completely change Naruto's character and abilities. Madara's teachings might lead Naruto down a darker path or give him incredibly powerful skills.