UPDATES 8/13: A lot more stuff on diffreent species, as well as added a fear section in the character profiles
There's no definitive guide for what a demon should look like. Most have horns, but this isn't certain (ex: Sitri and Overseer). In reality, a demon can really look like whatever. Most turn out like their parents, but even thats not certain for most demons, especially ones with shapeshifting parents.
Almost all demons have a "demon form" due to a genetic trait of the species, and the ones who don't are usually hybrids. Even without a demon form demons and demon hybrids are treated the same. Hybrids who do have a demon form tend to have less control over it, and have to be trained extra into adulthood.
A demon form reflects the user in many ways. It mostly reflects the user's mental state, and can become more unstable and dangerous the more unstable the user themselves is. This is why mental health is such an important part of the culture, to keep everyone safe.
It is also considered taboo to use a demon form in the presence of another species unless in private and with explicit consent.
Theres no definitive guide for what powers a demon will have upon birth, but they often derive from what their parents had (not 100% of the time though). When a new one is thought to be discovered, it is investigated and then written down in a book that stays locked away inside the Overseer's Castle (although copies exist for libraries and such).
Most powers also come at a cost, like a loss of energy or only being able to use one or two powers at a time. There's certain potions that are around to counteract that, but they're not used often.
Officially classified as whoever is directly related to the Overseer. This isnt many people, and does not include people married or adopted in, but currently includes Overseer, Atlas, Sitri, Mask, and Undertaker. Traits include heighted stamina and health, and the ability to use more abilities at one time. Each of the princes is enhanced in something (Atlas in strength, Sitri in smarts, and Mask in speed).