Seven Mysteries (七不思議) is a common trope in Japanese schools consisting of supernatural stories and happenings in school.
Kamome Gakuen also has a set of 7 mysteries.
Out of all 7, Hanako is the 'boss'. He maintains balance in the relationship between supernaturals in the school and humans.
Each Seven Mystery is more powerful than normal supernaturals in the school, and owns a yaishiro. They respectively have total command over a physical domain, where their power is at its strongest. It is called a boundary, a place where each seven school mysteries are unbeatable at. It was also mentioned that in the boundary, no one can die or be born. In addition, they can serve to oversee an aspect within the school -- and it is noted No.1 controls "Time", No.2 controls "Space", and No.5 controls "Records".
Shijima Mei notes that the Seven Mysteries are unable to disconnect from their rumors, which create set rules that the supernaturals have to follow without fail. For example, No.5 is not allowed to change the futures written in the books, and No.4 is not allowed to stop drawing pictures.