In a fanfiction about Tanjiro getting sick, it could be that he overexerts himself during a mission. His body gives in and he falls ill. His comrades take him to a safe house. While he is sick, he reflects on his journey so far, his losses and his goals. Meanwhile, the others keep a lookout for any danger and also try to nurse him back to health. They might face shortages of supplies and have to make difficult decisions.
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.
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.
Tanjiro's fate in the manga is that he ultimately passed away. This event was a significant part of the story's development and had a profound impact on the other characters and the overall plot.
Tanjiro's strength in the manga is significant. He acquires new powers and techniques, and overcomes numerous powerful foes with determination and strategy.