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.
For the most part, no. Manga creators usually want to deliver a coherent and focused story without the distraction of filler episodes. This helps maintain the integrity and appeal of the series.
Another interesting novel is 'Naruto Shippuden: Kakashi Hiden - Lightning in the Icy Sky'. It focuses on Kakashi's story and his past, which is really fascinating. There are a lot of details about his relationships and his growth as a ninja.
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.