Protection is a common theme. Tanjiro is always looking out for Nezuko, whether it's from other demons or humans who fear her. Another theme is loyalty. Nezuko's loyalty to Tanjiro is unshakable and this is often explored in fanfics.
Yes, there are some. You can check fanfiction websites like Archive of Our Own. Just search for 'naruto x nezuko' in their search bar, and you'll likely find a variety of stories written by different authors with different takes on this crossover.
One common theme is the clash of their different worlds. Naruto's ninja world and Nezuko's demon - slaying world can create interesting scenarios. Another could be the idea of them protecting each other despite their differences.
One popular 'zenitsu x nezuko fanfic' is 'The Unlikely Bond'. It beautifully portrays the relationship between Zenitsu and Nezuko. The author does a great job of showing Zenitsu's protective nature towards Nezuko and how Nezuko's presence calms Zenitsu in his often-fearful state.
One common theme is the development of their relationship. It often shows how Zenitsu's initial fear or admiration for Nezuko turns into deeper feelings. Another theme could be their adventures together, fighting demons side by side in some fanfictions.
Well, a lot of it has to do with the potential for character development. In the original story, their interactions are limited, but in fanfics, authors can explore how they would grow closer and influence each other. For example, Zenitsu could become more confident because of Nezuko, and Nezuko could learn more about the human side of relationships through Zenitsu. It's also about the fans' love for the two characters and their desire to see them in different scenarios together.
In the manga, Tanjiro and Kanao don't end up getting married. The story focuses more on their battles and character development rather than romantic pairings.