One common theme is self - discovery. Since Zenitsu has a complex personality, many fanfics focus on him finding out more about himself, his powers, and his place in the world. Another theme is friendship. He often forms strong bonds with other characters in fanfics, like Tanjiro and Inosuke.
Definitely not. In the manga, there's no such plotline of Zenitsu and Nezuko getting married. Their relationship is more focused on being comrades in the fight against demons rather than a romantic one leading to marriage.
Typically, tanjirou x zenitsu fanfic often focuses on their strong friendship. It might show how Tanjirou's calmness balances Zenitsu's more excitable nature. Also, their shared experiences in the demon - slaying world are a big part of these fics. For example, they might face a powerful demon together and their bond is strengthened through the ordeal.