Some gods might be curious. They would want to study the reincarnated character to understand how this reincarnation process happened. Others could be threatened. If the character has the potential to disrupt the power balance among the gods, they'll try to get rid of them. For example, Zeus might see the reincarnated character as a potential threat to his rule and act accordingly.
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.