Right then, time to start sharing the info that only you will know.
Firstly, the Chief Executives of the 5 Corporations funding the school will have elected you both as representatives of the School Council so if you can somehow tie that in to your background and why they would have elected you, meaning there must be some sort of connection there as they wouldn't just hire anyone.
There are many realms, realities and dimensions out there that exist beyond the boundaries of this world. Sometimes, the barrier can be sufficiently weak that people can interact with these places and even summon things from other realms or dimensions. It is not a normal occurrence in this world, which is why such things aren't common.
Heaven and Hell are but realms that exist beyond our own, at times people have been able to see through the boundaries to realise the truth. However, there are different realms that could be seen as Heaven, different realms that could be perceived as Hell and a vast array of other realms out there people have never realised existed.
In one realm, that could be seen as a Hell Realm there exist powerful beings there known as the D'Rathumal, which to this world would equate to being a Devil or a Demon. The Headmaster is one of the D'Rathunal from this realm along with the island.
The D'Rathunal are immortal and feed off of the chaotic and fluctuating energies around them. The D'Rathunal had limited ability to travel between realms but like all immortal beings boredom had a way of setting in. Needing something new, one D'Rathunal performed a ritual that would open a gate to a completely different world so that he and his people could have a new world as their playground and amusement. The Gateway between worlds opened but due to the number of worlds and clashing energies, the ritual was not perfect and ended up with an unintended result.
The Headmaster's true form is lost between realities but he was able to partly stabilise a piece of land he had performed the ritual on in a new world, that being Earth. Along with establishing the island on Earth, some of his essence became attached to the island allowing him to morph that essence in to a physical form, that being the Headmaster. He still has access to his powers and due to his true form being trapped between dimensions, his form as the Headmaster can't be hurt or killed in any way.
The Headmaster is now completely trapped on this island but can still use his powers and travel between realities though it can be a strain.
The Headmaster needed to form alliances with humans in this world and so he began forging contracts with people and lending them his power in return for their allegiance and to help the Headmaster in his quest to retrieve his true form, merge with it and use his power to make this world his new playground. Humans had a very chaotic nature and he very much liked the taste of them so far but he wanted to fill this world with more chaos.
Corporations were set up on the island to fund a school that would be run by the Headmaster, the heads of these Corporations would be under one of the Headmaster's contracts leading these corporations to perform extremely successfully in a short space of time.
The School was set up to bring the brightest talents from across the world to help further research and development that could help the Headmaster locate his true form.
The Headmaster found people at the school who he thought possessed certain skills, traits and abilities that could be most useful in helping him on his mission. In return, they would become members of the school council and would be given contracts that would lend them his strength and power making them stronger than any other normal human.
As members of the school council, they would be granted supreme authority second to only the Headmaster and upon retrieving his true form he has promised to give these people anything they could want in return.
The problem now exists tha there are many people on this island who every night develop super powers that could interfere with his plans or ruin everything he was trying to achieve. The Headmaster could not allow this and kept the truth to just a select few people he believed he could count on. If others knew the truth, they could all turn on him in an instant or destroy the island that binds his essence to this world. Were the island to be destroyed completely, his essence would join his true form lost forever between dimensions and this was something he did not like the thought of.
Every night, when the school goes out of phase with this world, it is trying to reconnect to the Hell Realm it originated from but doesn't have the power to do so though although there is a great amount of energy from all of the other dimensions it is colliding with, the greatest source of energy and power fluctuating through the island is that of the Headmaster's own home Realm, therefore, what is really the true source of rising the abilities of everyone on the island is demonic energy from the Headmaster's home Realm.
Although the Headmaster realises that rules, order and discipline are necessary to run the school, he really enjoys nothing more than a good dose of chaos to feed off of, so he finds great satisfaction and amusement when he sees all the trouble people can get up to. What he finds most amusing is the fact that the more rules are enforced the more people want to break them. However, keeping people in line and under control when required is also needed. Hence, giving teachers authority to control unruly students and the School Council Taskforce to make sure people are kept in line and behave properly. After all, should the students and teachers be given too much freedom and leniance they may accidentally stumble upon the truth and that is the last thing the Headmaster wants.
So, this is really the basic summary of what is going on behind the scenes. The Headmaster is a Demon and I'm sure many people have had these types of thoughts before.