1. Witches for the most part lead hidden lives, they generally don't want people to know they're a witch. There are indeed covens, and if there are not covens, hopefully your mother, or a rare case of father witch is there to help teach you how to control your powers. There is also the mechanical benefit that a witch's power isn't elemental in nature, but witches that gain a vision can change that. Much of their traditional arts are ritual and brewing based, but they also have things like polymorphing, animation, and even familiars. As for a connection to an element based on race, well, there is none.
Nations of each element are defined as such because their lifestyles and culture revolve around that element, the element that their Archon presides over. Being surrounded by that element most of one's life can have an influence naturally, but it's not set in stone. You could be a cryo witch if you like while being born and raised in Averton.
2. So Cryptids and Noble Beasts in particular are inspired by things of the same nature we know, vampires and werewolves for Noble Beasts, and Chupacabra and Loch Ness for Cryptids. The nature of their powers are also different. Cryptids use mystical power which is rooted in the unknown, while Noble Beasts use ectoplasmic power which is rooted in spiritual energies. Yaoguai are a bit more general, but their closest comparison is the Yaksha from the game, however instead of being created as almost god-like protectors, Yaoguai are wildlife spirits, and can become greater spirits by transcending their common mortal forms. On the surface it's a lot of flavor, but when you want to play any of them and wish to go deeper, there's unique lore for different paths.
3. Playing a full Adeptus has a great deal of limits, so it's more than likely a full Adeptus won't be playable in the end. Those limits include being secluded to one or few locations, not interfering in worldly affairs, and so on, in exchange they get their own pocket dimension, their own domain. In such cases if you want to be an Adepti, play a half instead. While halfs are unable to maintain their own domain, they can use the creation arts of the Adepti.
As for the Shaitan, the level a player would be at is able to imprint words and phrases in people's mind, have their opinion lean slightly a certain way, and so on. They won't be able to explicitly or strongly push someone to do something erratic or seemingly unprovoked like in their legends. For your suggestion to work, some semblance of what you want them to do needs to already exist in their mind. Shaitan are more effective the less decisive someone is about something. They're not sure if they want to eat beef or chicken? It's almost free that you can tell them what to eat for lunch. On the other hand if they're dead set on eating beef, you won't be able to convince them to eat chicken with your powers alone. Hopefully that all makes sense.
I'll also remind that these are the much rarer races, and most of the time don't hold high stations or even certain professions. Humans and beast people still hold much more normal professions. There's also an elf-like race in Genshin, so if that's also your thing then sure go for it. I'll probably have them in too. I'll have a small list for these three soon enough.