In novels, the Prince of Demons usually did not directly PK the Princess because the Princess was usually a character in a novel or anime that represented a specific country or power, while the Prince of Demons was another character that represented a different power or goal.
In some novels or anime, there might be a battle between a demon prince and a princess, but it was usually because of a conflict of interest or goals between the two parties, not because the princess herself had evil characteristics. Therefore, the plot of the Demon Prince vs. Princess might appear in specific novels or anime.
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.