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.
Inosuke doesn't become a Hashira in the manga. The story progresses with him having other significant experiences and achievements instead of achieving that specific position.
It's hard to give an exact number. Different story arcs and battles led to the deaths of multiple hashira. Some died heroically, while others met their fate in unexpected ways. The count changes as the manga progresses.
Definitely not. Genya remains outside the ranks of Hashira throughout the manga. This is because of a combination of factors such as his skills, experiences, and the overall direction of the story.