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.
One possible plot twist could be that Tanjiro has to sacrifice a part of his own power to save Rengoku. Maybe he has to give up some of his newly acquired breathing techniques which he has worked so hard to master. This would show his selfless nature and his deep respect for Rengoku.
One common theme is adventure. Since both characters are from the Demon Slayer universe, they often go on demon - slaying adventures together in the fanfictions. They might face powerful demons and rely on each other's skills to survive.
You can try fanfiction platforms like Archive of Our Own (AO3). There are a large number of fan-created works there. Just use the search function and type in 'female Tanjiro x Rengoku' and you'll likely find a variety of stories with different themes and writing styles.
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.
The Hashiras would likely show concern. Some, like Shinobu, would immediately start looking into possible medical solutions. Giyuu might be more reserved in his worry but would still keep a close eye on Tanjiro. The other demon slayers would also be affected. They look up to Tanjiro, so his sickness would lower the morale of the group. They would try to support each other while waiting for Tanjiro to recover.