Hmmm... Feel like there might be a bit too much lore available to the characters.
What I mean is, if the supernatural phenomena is new or somehow rare/difficult to observe, then it's very reasonable for there to only be basic rules for dealing with it.
But if they've got decades and decades of reports on these mysteries then:
Inhales
Do mysteries reappear and if so how often? What happens if you purposefully record inaccuracies? Conjectures based on similar mysteries? Are there any apparent categories? Are there similarities between successful and failed reports respectively? Does a failed report affect mysteries in the area? What happened to graduated duty members? Is there any pattern to the deaths of duty members? Can moving things around during the day affect classrooms at night? Do mysteries require senses (sight, hearing, etc.) to take effect? What kind of details inhibit growth the most? Are there records of incidents where mysteries entered the real world?
The answers to these and many more questions can be answered.