1) To kill a person with a Death Note, you need to write in their SEN name and their pseudonym, and you must know what their face looks like (edited for this mafia)
2) After you write the name, you can write the time of death and a descriptive narrative of their death stating what they will do before dying, how they will die, who will they meet, etc. With the Death Note, you can control not only the person, but also the thing that will cause their death. For example, you can write something like "Aristocrat 4 PM killed by Walter stabbing him in the eye by mistake". If a time of death is not specified, the person will die within 40 seconds.
3) After you misspell the name of your victim(s) (aka write a name that does not belong to the person whose face you are picturing while writing into the Death Note) four times, the Death Note will become useless. You can, however, misspell the name of a dead person as many times as you want without impunity.
4) The owner of a Death Note might make a contract with a Shinigami to obtain eyes that can see any person's name hovering in front of their face.
5) You can enter the time and details of death before writing the name of the victim. However, once you write the name, you only have a few minutes to write the details of the victim's death.
6) If the things you wrote as the details of the death will directly cause additional deaths, the victim will be killed by a heart attack instead. However, if the things you write in the Death Note alone cannot cause more deaths than the person you wrote, you can manipulate those things physically to cause more deaths (refer to the killing of the FBI agents in the manga/anime)
7) People under 780 days old are not affected by the Death Note (just in case Aristocrat takes SEN joining date into account )
8) You can relinquish control of the Death Note and transfer it to a new owner. If you do so, all your memories concerning the Death Note will vanish unless you own yet another Death Note, and you will become the same person you would be if you have never received the Death Note. These memories will temporarily return if you have physical contact with a page of a Death Note, or if you receive ownership of a Death Note.
9) Each Death Note is haunted by a Shinigami, the original owner of the Death Note. Only the owner of the Death Note and all the people who have touched a page of that Death Note can see that particular Shinigami. Upon relinquishing control of a Death Note, the ability of seeing the Shinigami will also be lost unless the person owns another Death Note. (not sure if this game has Shinigami )

I think that's all that matters :3