Well, he could either find it hilarious or a bit offensive, depending on what the fanfiction is about. If it's a comical take on his story, he might laugh his head off. But if it distorts his relationships or his character in a negative way, he might not be too happy. For example, if someone writes a fanfic where he's a coward, which is completely against his real personality, he would likely be annoyed.
He might be really surprised. Some fanfictions could have really out - of - the - box ideas that he'd never thought of. For example, if there's a fanfiction about him having a different kind of training with a new teacher, he'd be like 'Whoa, that's a new take on things.'
Well, Minato might be proud to see how his son Naruto has been portrayed in the Naruto Shippuden fanfiction. He could also be impressed by the creativity of the fans in coming up with new storylines. Kakashi would likely enjoy reading different takes on his own character and the battles he's been in. Rin would probably be excited to see how her character has been explored in different ways, whether it's her relationship with Kakashi or her role in the overall story. Obito might have mixed feelings. He might be angry if the fanfiction misrepresents his motives, but also intrigued if it offers a new perspective on his journey.
Sure. The characters are a huge part of Naruto Shippuden fanfiction. Fanfic writers use the characters to attract readers who are fans of those characters. They might focus on a character's backstory that wasn't fully explored in the anime and expand on it. Also, the interactions between characters in the original show give fanfic writers ideas for different scenarios in their stories.
By their unique abilities. Naruto's Rasengan, Sasuke's Sharingan, these abilities can be the starting point for many fanfiction ideas. Writers can think about how these abilities could be used in different battles or situations not shown in the original.
One of the most popular is 'Naruto Shippuden: Sakura Hiden - Thoughts of Love, Riding Upon a Spring Breeze'. It's popular because it shows Sakura in a new light, with her own adventures and growth.