The purple pigment makes their teeth marginally harder, and thus wear down slower. There is a lot of variation between individuals but lighter teeth are more common in settler populations (who have a softer diet) and darker teeth are more common in nomadic populations. Obviously not a hard rule though because Talita, for example, is quite sunchaser nomad in appearance but has light teeth. Maybe she has some Shess ancestry, who knows.

Because they wear down slower, a centaur with dark teeth and an unchallenging diet will have more issues with tooth overgrowth and will need to file them more often.

It’s just a slightly concave stripe of dark feathers on their face. The vast majority of centaurs possess it because it improves visibility and reduces sunlight glare when looking down the snout. It has the same function as the eyeshadow markings on albatrosses (and many other animals) and the black paint face paint on outdoor athletes.

Many centaur clans would choose to cull an abandoned human infant if they couldn’t find a human willing to take it. Haha, that would be a political nightmare. The centaurs would think of it as kinder than allowing the infant to grow up under probably traumatic and physically unhealthy circumstances, avians/humans/bug ferrets would consider it pretty monstrous. (They fact they all have much fewer infants per pregnancy, lower disease-related infant mortality rates, and much better access to reliable birth control is surely unrelated.) I think given the circumstances on the centaur homeplanet a reverse Talita situation would be exceedingly unlikely to happen. Talita was also exceedingly unlikely to happen, but areas where homeplanet centaurs have access to human food are right next to areas with a human embassy, and the kid would probably immediately get handed over to the embassy.

Also, I think many centaurs would find baby humans cute the same way humans find kittens cute. Ironically it’s easier to find other species’ babies cute when they don’t cry in a way you’re hardwired to pay attention to, aren’t gross in an uncomfortably familiar way, don’t have any of your uncanny valley triggers, and aren’t associated with heavy reproductive and childcare investments.

No to the first two questions and the last one you can read about on the website. Centaurs are much less prone to large unified governments than humans due to the isolationist and quasi-political nature of their family hierarchies, in addition to having a much lower global population than humans of an “equivalent” technological level.

jayeaton.site/RunawayToTheStars/Sophonts/Centaurs/Culture#Politics

They stop eating nutritional silk after they pupate. Imagos eat regular foods, such as bugs and raw meat. Some cultures use discarded cocoons in fibercraft, but they are not a hugely abundant resource. They’re not really edible, cocoon silk is not nutritious and mostly composed of tough difficult to digest fibers.

They can do the exact same thing elephants do, which is suck some water into the length of the trunk and squirt it into their mouth. They have a much shorter trunk, though, so it isn’t terribly effective. Centaurs primarily use their trunk as a vocal organ and fine manipulator.

Yeah all the centaur ethnicities are the same species, like human ethnicities. Nomads and settlers could possibly be defined as subspecies (in that they are phenotypically distinct populations with low gene flow between each other) but they can still easily hybridize with no issues.

Your second question is also in my FAQ.

I think you may be imagining that wild stock/game is being kept the same way that livestock is, which isn’t the case.

Gamekeeping (the work of maintaining a population of wild prey animals) is an aspect of land management. Settled centaurs tend to have large territories of land that they hunt and forage in which they directly manage through controlled burns, tree cutting, planting, terraforming, driving off and killing carnivore competitors, and discouraging the growth of plants and animals they have no use for. Nomadic centaurs don’t manage a specific area of land, but tend to sculpt the areas they travel through over time in similar ways as their livestock herds range on them. Unbalanced range management can result in its own sort of monoculture, and disease or overhunting related population crashes. Balanced range management can result in a highly productive (read: producing things centaurs like to eat and use) area of land with much less labor involved than livestock keeping. Livestock is a lot more work, because you’re directly responsible for the care, husbandry, and feeding of the animals.

This a phenomenon I didn’t make up, humans also keep wild stock in combination with livestock for food. Wild stock is frequently a very important food source for rural communities in real life.

It’s an antler pedicle.

Because they’re on her jaw a lot of people refer to them as her tusks, but the structure is wildly different. Readers keep asking me if she could file them down, but a growing antler has skin over it, a large blood supply with lots of veins, and an unmineralized tip. It would be like trying to trying to file down your elbow. Cutting off the growing tip may halt growth, but, it would be very bloody and there’s a chance it would continue to grow anyways in a deformed shape. For centaurs, even the mature, bare antler has a central blood supply down most of its length.

Yep. Or two upper torsos.