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.
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.
Kisame himself would obviously be a main character. He's the center of the 'legacy' aspect. Also, characters like Itachi Uchiha are likely to be important since they had a significant relationship with Kisame in the original Naruto story. Naruto Uzumaki could also be a key character as his story is so intertwined with the overall Naruto world and Kisame was part of the Akatsuki that Naruto had to deal with.
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.
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.
In a fanfic of Kisame and Itachi taking Naruto, it might explore the relationship between the two Akatsuki members and Naruto. Itachi has his own complex reasons for his actions, and Kisame is his loyal partner. When they take Naruto, Itachi might be conflicted as he has a connection to Naruto through Sasuke. They could end up in a situation where they have to make a choice about what to do with Naruto.