Nope, just made up. There is no such otome game. I heard that whoever started this actually never played otome game before, and that they created the villainess genre to mock otome game players. That might explain why Japanese otome players are quite defensive and sensitive whn it comes to otome...
No. She happened to like that other girl, and was saddened to find out that she has a boyfriend, hence the killing. There was a panel that focus on said boyfriend's message.