I'm not sure specifically as there could be many novels with a name like that. Generally, it might involve a story where the main character has to take on the role of killing villains. Maybe there are complex battles, moral dilemmas, and character growth throughout the story.
Yes, Kill la Kill originated as a manga. It gained popularity and was later adapted into different mediums, with the anime being particularly well-known.
Since I haven't read it, I can't say for sure. But typically, there would be a protagonist who is the one aiming to kill the villains. There might also be sidekicks or allies that help the main character in their quest.
Well, when a villain meets a villain in manga, it can result in all sorts of scenarios. Sometimes they might try to outwit each other, and other times they could find common ground and work together, but with hidden agendas.