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.
Tanjiro might use his sense of smell to detect hidden threats. Since his sense of smell is super - enhanced, he could sniff out any demons or traps in the way of saving Rengoku. For example, if there are demons disguised as allies, Tanjiro would be able to tell by their scent.
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.
Yes, in some fanfictions, Tanjiro is depicted as the reincarnation of Yoriichi. This concept adds an interesting layer to the story as Yoriichi was an extremely powerful and legendary figure in the original lore. The idea allows for new storylines where Tanjiro might inherit some of Yoriichi's skills or have a deeper connection to the past events related to Yoriichi.