One common theme is family loyalty. Given the strong bond within the Kamado family in the original story, this is often explored further in fanfiction. Another theme could be redemption, especially when it comes to Nezuko's situation as a demon. Writers might also focus on the theme of survival, as the family has to deal with the constant threat of demons.
Demon Kamado family fanfiction can be really exciting. It could focus on the untold stories of the Kamado family. Maybe there are stories about their ancestors and how certain family traits were passed down. Some fanfictions might also create alternate universes where the family has different powers or face different types of demons. It gives fans a chance to expand on the original story and get creative with the characters and their relationships.
As of now, Uta is indeed alive. The story hasn't depicted anything otherwise. Maybe there'll be changes in the future, but for now, Uta's part in the manga continues with them being alive.
Nezuko is initially 12 years old in the manga. As the story unfolds, her age doesn't change significantly in a traditional sense, but her character development is quite remarkable.