Kagome adapts by using her knowledge from her own time. For example, she might use her medical knowledge (if she has any) to help those in need in the Inu no Taisho era. She also has to adapt to the different social norms. Since she's from a more modern time, she has to be careful not to break the unspoken rules of that era. Another way she adapts is by learning the language and customs quickly. She may observe others and ask questions to fit in better.
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.
Well, in a 'Naruto in Taisho period fanfiction', the characters' outfits would change to fit the Taisho era. Naruto might wear a traditional kimono and hakama. The village of Konoha could be transformed into a more feudal - like settlement, with different social hierarchies and customs. Also, the jutsus could be depicted as ancient arts passed down through generations in that period.