Kisame would probably be very angry at first. Samehada is his weapon and has been with him for a long time. He might feel betrayed and try to get Samehada back by force.
Iruka could be an important character. He's always been like a father figure to Naruto, and now with this new revelation, he might have to help Naruto deal with it. Hinata could also be in the story, and her feelings for Naruto could be complicated by his connection to Kisame. And then there could be some original characters created just for this fanfiction, like a ninja who was a former ally of Kisame and has some information for Naruto.
There could be. Fanfiction is a vast realm where all sorts of ideas are explored. However, I'm not sure if there is a highly popular or mainstream 'naruto is kisame apprentice' fanfiction. It might be a more niche concept, but it's entirely possible that some creative writer has delved into this idea to create an interesting story about Naruto learning from Kisame, perhaps incorporating Kisame's unique fighting style and view of the ninja world into Naruto's growth.
At first, it would be full of suspicion. Naruto is a Konoha ninja and Kisame is from the Akatsuki. But as the teaching progresses, they might develop a mutual respect. Naruto would respect Kisame's power and knowledge, and Kisame might respect Naruto's determination.
A 'Solar - Flare Rasengan'. Naruto could combine his wind - style chakra with some kind of solar - based energy he discovers. This jutsu would be like a super - charged Rasengan that emits a blinding light as well as powerful wind - based damage.
There could be a jutsu that allows for instant teleportation across long distances. This jutsu might be a new discovery in the fanfiction world, perhaps created by a character who has been experimenting with space - time ninjutsu. They might use it to quickly get in and out of battles or reach far - off places in a blink.
Well, in some fanfictions, Naruto might defeat Kisame in a battle and take the sword as a trophy. Maybe he uses his newfound Sage Mode powers or some other advanced jutsu to overpower Kisame and claim the sword.
One idea could be a story where Naruto and Kisame are forced to team up during a mission that has a greater threat to the ninja world. They start off distrusting each other but gradually come to respect one another's skills.
It could be a new form of Rasengan. Maybe Naruto discovers a way to combine different elements with the Rasengan more effectively, like adding lightning to it for a more powerful and faster attack.
There's also the 'Inferno Storm Jutsu' in some fanfictions. It creates a large - scale storm made entirely of fire. The fire in this storm has different intensities, with the center being the hottest and most destructive. It can cover a large area, making it a great offensive move against groups of enemies.