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.
No. There are important events in the Naruto universe that are not covered in Naruto Shippuden. Some of the earlier history of the ninja clans, for example, is only hinted at in Shippuden but not fully explored. The full story of how certain jutsu were created and passed down through generations is also not completely told in Shippuden.
Naruto is obviously the most important. Sasuke is also crucial as his relationship with Naruto drives a lot of the story. Kakashi is Naruto's mentor. Sakura is Naruto's teammate and she has her own growth arc. Then there are villains like Madara and Obito. Also, characters like Jiraiya who plays a big role in Naruto's training and development are important in the Naruto Shippuden life story.
Naruto is definitely one of the most popular. His journey from an outcast to a hero provides a lot of material for fanfic writers. Sasuke is also very popular as his complex character and his relationship with Naruto are always interesting to explore. Hinata is quite popular too, especially in fanfics that focus on her love for Naruto and her own growth as a ninja.
Sasuke would likely be more critical. He'd scoff at some of the fanfiction that portrays him inaccurately. But he might also secretly enjoy the ones that show his growth and development in a new light. He'd be all like 'This one has some truth to it, but this other one is just nonsense'.
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.
Shikamaru can be a great character to pair with Ino. Their long - standing friendship and shared experiences growing up in Konoha make for an interesting dynamic. They understand each other's quirks and can complement each other in battle and in decision - making.
Pain is often a very popular character in Rinnegan fanfiction. His original use of the Rinnegan in the series made him quite an interesting character, and in fanfiction, people like to explore his backstory further or give him new powers. Nagato, who was the original owner of Pain's body, is also popular. He has a complex history and his connection to the Rinnegan can be explored in many ways.