Not sure why people are confused. The premise, such as it is, was clearly explained on page 6. The school nurse is basically functioning as a type of "secret police", empowered by the school board to quietly handle any untoward incidents. The fact she is herself a blazing lesbian and doing it with a student is par for the course. There was nothing supernatural, Saegusa just has a forceful (and somewhat psychotic) personality. As an undesirable element, she was investigated and eliminated by Sensei and her deputy detective Anko.
I was actually really enjoying it until the rough stuff/dubious consent started. Maybe subsequent chapters will improve on that, but if I know anything about multi-chapter ecchi, it's that it tends to escalate with time...we'll see.
Thank you for your efforts, Yuri Project.
Thanks for clarifying, makes a lot more sense now.