Random facts and headcanon:
-Eiki was once a Jizou statue. Jizou statues were Buddhist statues put at the side of roads for the protection of travelers, women, and children. They're nature is to help those in need and encourage inspiration and enlightenment.
-She is a minor judge in the court system of Hell, and reigns over Paradise which is the court in charge of Gensokyo. She is part The Ministry of What's Right and What's Wrong.
-Despite being a minor judge, she is labeled as both the Supreme Judge of Paradise and Supreme Judge of Hell. It's safe to say that her position is only "minor" in comparison to The Ten Kings.
-Yamaxanadu or Yama Xanadu is her title, and should not be confused with a last name (that is Shiki). It means Yama of Paradise, or Judge of Paradise, and refers to Gensokyo. Though, despite her title being specific to Gensokyo, she has jurisdiction in the outside world as well, possibly areas near where the border was created. Since she is a yama, the border between Gensokyo and the outside world means very little to her.
-Minor judges are below the 10 Kings of Hell, and below them are minor demons and shinigami, below the shinigami and demons are the oni of Hell.
-One could say the only higher authority than Eiki are the 10 Kings, if they're involved in something that would be pretty bad though.
-Usually yama have very high risk warnings, but since the likelihood of encountering one is low, it's not something people worry about. Generally if one is about something is very very wrong.
-Despite yama in general having high risk levels, Eiki has very low risk due to the fact she doesn't actively want to do anyone any harm. One could say her spell cards and actions while using them does not reflect well on her abilities as a yama, but more reflects her personality and wish to support people for a better life style.
-It was once said by Yukari that Yuyuko, Reimu, and Yukari herself combined were no match for Eiki.
-The fact that Komachi continues to have a job is proof that Eiki is very lenient, despite lecturing all the time. The fact that it was said that if Komachi ever did lose her job it would be very difficult for her to get a new one, says quite a bit on Eiki's temperament.
-Eiki has more subordinates than just Komachi, including demons and other shinigami. She worries more about Komachi due to Komachi's slacker nature though. Everyone else does their job as told so aren't concerns.
-Since Eiki is not a part of Gensokyo and is not from it, she has access to other places beyond it, such as the outside world. She doesn't go there though, as she has no reason to deal with it.
-Both Eiki and Komachi have shown extensive knowledge of the outside world due to the fact that their jobs are not restricted to Gensokyo residents exclusively. But due to the nature of their jobs, their information can be behind by quite a bit.
-Eiki when visiting Gensokyo abides by the Spell Card rules because it is the correct and respectful thing to do while there, but otherwise is not bound by it.
-In general Eiki doesn't get out a lot due to the amount of souls she must sentence, but she does get breaks, and every once in a while Komachi causes a backlog that frees up Eiki's schedule. Usually when this happens she goes to see what Komachi is doing so she can punish her for slacking.
-Eiki's court is the only court that runs erratic and does not keep a steady flow of souls, this is due to Komachi's work ethics though.
-Despite the fact that Komachi gives Eiki a bad name, she won't fire her, and continues to believe that discipline measures will somehow wake her up to being model employee.
-When Eiki doesn't have work to do, she feels lost and is thus compelled to go visit the living to warn them of their sins and lecture.
-She really likes lecturing so doesn't mind it when she can go about to do it, she really sees it as helping.
-The best thing to do if you are caught in a lecture with her is to either run away, or present a more important topic. It's easier to run away, start a fight at your own risk.
-Despite being rather old, and having a distinguished position, Eiki's experiences outside the court room are very few, and her life experiences are next to nill despite having a lot of knowledge on how the world works.
-Most people who know her use her full name, yama or enma when referring to he out of respect, as it is bad form to be disrespectful to a yama.
-There are stories of yama doing various things at will, such as restoring particularly virtuous people to their existing life, and cutting short particularly sinful people who have insulted them. Though Eiki is fully capable of these things as well (within her jurisdiction), her nature is mostly against it.
-Eiki has a strong and powerful aura about her, and for those who can sense such things will feel intense power when she enters an area. This is what most youkai feel when she enters an area, this gives them a head start when avoiding her.
-Despite fanon depicting her as incredibly short, Eiki is actually of a good height. It is debatable if she is taller than Komachi or not, but she is definitely closer to Komachi's height than popular depictions. She is also not utterly flat, though she tends to wear clothes that that give a reduced appearance. She is still thin and of a thin build.