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.
Perhaps Naruto has a different fighting style that Samehada finds more appealing. Naruto is known for his unpredictable and energetic combat, and Samehada might be drawn to that. It could also be that Naruto has a certain charisma or willpower that Samehada responds to on a more instinctual level.
In the fanfiction, it could be that Kisame gives Naruto Samehada as part of a deal. Maybe Naruto has to do something for Kisame in return. Naruto might struggle with the idea of making a deal with an Akatsuki member but decides it's worth it for the power of Samehada. Once he has it, he might face opposition from his friends and village elders who are suspicious of his new weapon and the way he obtained it.
The plot could involve Naruto using Samehada to gain an understanding of the Akatsuki's motives. Since Samehada has a connection to the Akatsuki through Kisame, it might hold some secrets. Naruto could use it to track down other Akatsuki members or find out more about their plans.
Another way is that Samehada might be given to Naruto by a mysterious figure. This figure recognizes Naruto's potential and believes that he can handle the power of Samehada. This then sets off a chain of events where Naruto has to learn about and master Samehada's abilities.
In some fanfictions, Naruto might gain the ability to absorb Samehada through a special encounter. Maybe he discovers an ancient jutsu that allows him to connect with Samehada on a spiritual level and absorb its power.
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.
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.
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.
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.