HEAT HAZE:

The Heat Haze Daze is a never ending world, created by Azami, who originally intended to live in this world with her family, due to the fact that humans age much faster than gorgons and would mean that her husband Tsukihiko, who was a human, would have to die long before her time. However, their home was attacked by the villagers immediately upon creating it, so she came to believe that unhappiness comes when she is involved with humans. She ultimately decided to enter the Heat Haze Daze alone and live there in eternal solitude.[1]

However, time passed and her daughter Shion, as well as her grand-daughter Marry were murdered by humans and swallowed by the Heat Haze Daze. Wishing for at least her grand-daughter to live, Azami gave her the Queen of the Snakes, also know as the "Snake of Combining Eyes", which would serve as a surrogate life for Marry, while Shion lost hers.

Azami lost her ability to unite the snakes, so she became unable to undo the order she gave to the Heat Haze Daze: "Bring in the people who died on August 15". To enter the Heat Haze Daze, a living creature must die on that date. It is possible that one of the snakes possesses them, acting as a surrogate life and making them receive an eye ability, which makes it possible for them to leave the Heat Haze Daze again, while in some cases they do not receive a snake and remain inside the Heat Haze Daze, unable to leave pretty much.
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EYE ABILITIES:

Eye Abilities are powers given to a person who has entered and left the Heat Haze with a snake as their surrogate life. Each eye ability is different, although each of them are given to a person by one of Azami's snakes.
The abilities are usually influenced by an important part of the owner's life before their death (i.e. Momo wanted more attention for herself and received an ability that would gather all attention on her). When the abilities are activated, the users' eyes turn red and become similar to those of a snake.
Countless black snakes with deep red eyes grow from Azami's head as her hair, which is a typical feature of a gorgon. These snakes, however, are intelligent creatures on their own, the most intelligent one being the Snake of Clearing Eyes, which is the snake that gave Azami the idea of the Heat Haze Daze in a dream she had. As Shion and Marry were murdered by humans and swallowed by the Heat Haze Daze, Azami gave Marry the Queen Snake, which is able to control all the other snakes, so she would be able to make it out again.
The loss of their queen Snake enraged the snakes enough to make them overthrow Azami under the lead of the Snake of Clearing Eyes, as she was no longer able to control the never ending world without it. Since the Queen Snake would now live in the real world, the snakes planned to possess the bodies of humans who entered the Heat Haze Daze, in order to follow their queen and create a new medusa/gorgon in the outside world.

SNAKES(THE ACTUAL POWERS):

Queen Snake / Snake of Combining Eyes: Marry
--Marry's ability allows her to temporarily stop the movement of whoever meets her gaze. It is not as complete as her mother's or grandmother's power as she is not able to turn people into stone, but to more "freeze" them.
Marry also has the ability to "combine eyes" with the others snakes. It was given to her by Azami as she entered the Heat Haze.

Snake of Concealing Eyes: Tsubomi Kido
--Kido's ability can divert perception towards objects and even people within two meters of herself and/or her surroundings, rendering them invisible. Conversation while being hidden also won't be heard by outsiders. Physical contact, however, breaks the effect, so it is not useful in very crowded places. Along with this vulnerability, if a person outside the two meter bubble is familiar with someone being concealed, her power will not be as strong. Kido's ability works more when preventing people from recognizing those being hidden, rather than making them unable to be seen. She has practiced to control her ability perfectly and to not disappear all of a sudden.

Snake of Stealing Eyes: Kousuke Seto
--Seto's ability allows him to read information from the target's mind. He can also speak to animals using his eye ability.

Snake of Deceiving Eyes: Shuuya Kano
--Kano's ability can change what people around him see and show them something different, but he can only use it on himself, means he cannot change appearances of others or similar.

Snake of Captivating Eyes: Momo Kisaragi
--Momo's ability can draw peoples' attention, regardless of their preferences in tastes or interests.

Snake of Opening Eyes: Takane "Ene" Enomoto
--Ene's eye ability is known as the "Opening Eyes", which allows her to be immortal and to transform into a cyber-being. After regaining her human form as Takane, she also possesses the power to control electronic systems, as her cyber-self did. While using this power, her body temporarily loses its consciousness.

Snake of Focusing Eyes: Hibiya Amamiya
--Hibiya's eye ability has the power to perceive objects and details that are far away from an aerial view.

Snake of Awakening Eyes: Haruka "Konoha" Kokonose
--Konoha's ability gives him the power to remake his body into one that he finds to be his "ideal" - as Haruka was physically weak and sickly, this meant for him to become supernaturally strong. However, this puts a large strain on his mind, and causes him to lose part of his memory.

Snake of Clearing Eyes: Kenjirou Tateyama, Black Konoha, Hiyori Asahina
--Kenjirou's ability lets him interfere with and stop the use of other eye abilities completely.

Snake of Favoring Eyes: Ayano Tateyama
--Ayano's eye ability allows her to project her emotions onto others, which she refers to as "the power of caring".

Snake of Retaining Eyes: Shintaro Kisaragi
--Shintaro's eye ability, given to him by Marry after promising long ago to "never forget this tragedy", allows him to remember everything he sees, including the events of past routes.