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.
One common theme is friendship. Female characters often form deep friendships with Zenitsu, helping him grow and overcome his insecurities. Another theme is adventure. They go on demon - hunting adventures together. For example, in many fanfics, they explore new regions in search of powerful demons.
Definitely not. The story doesn't depict Zenitsu and Nezuko as a couple. Their paths in the manga are more about their individual quests and battles against evil.