Yes, after several hours spent following links on Wikipedia and various websites giving advice on raising and looking after horses, I give you a serious, academic treatise on the natural biology of... the centaur. You know, like Dawn turns into in Season 8, although most of what I say should be applicable to centaurs from other fantasy and mythological sources.
If you're squicked by the use of terms such as 'digestive tract', 'oestrus' or 'trachea', you may not want to read this. If you're a qualified veterinarian, horse-breeder, doctor, or indeed a majestic creature of legend yourself and spot any errors, please feel free to correct me. The rest of you... I advise you to shake your heads sadly and move on quickly to the next post in your friends list. That'll be better for all of us in the long run.
On the Natural Biology of Centaurs
A centaur is a creature made up of the upper body of a human merged with the lower body of a horse. The human torso extends about as far as the navel - and the pictures of Dawn in S8 show that she does indeed have a navel there, which raises some interesting questions about centaur gestation. The horse body extends from the base of its neck downwards.
Obviously such a creature is magical in origin, and its bodily functions may depend to a greater or lesser degree on magic to even operate. However, for the purpose of this essay I will assume that where both a biological and a purely magical 'handwave' solution exist for the same problem, the biological one will be preferred.
On first glance, a centaur's organs can be divided neatly into 'human' and 'equine' categories. However, closer examination shows that this cannot be entirely the case. A centaur only has one brain, in its human head; but this must control the autonomic functions of the horse body as well. A centaur has to coordinate six limbs - two arms and four legs - not just four. In short, a centaur's brain is not identical to a human brain. My assumption will therefore be that for the most part the human and equine organs operate as they would in a person or a horse, respectively, but where necessary there will be unique centaur features.
Circulatory and Nervous Systems
Like Timelords, centaurs have two hearts. I assume the blood circulates throughout the entire body, rather than having separate circulatory systems for each section.
As described above, the centaur's nervous system is controlled by a single brain, in the human section. However, the spinal column extends into the horse section, and I assume the nerves are integrated. Dawn experiences the sensation of pulling her mane in the same way as she does pulling her hair. We can assume that other forms of touch will work the same way regardless of whether the area contacted is human or equine - making allowance for the fact that in general a horse's hide is thicker and less sensitive than a human's skin.
Respiration poses more of a problem. The human lungs work the same way as those of a normal human. However, there is no obvious way for air to reach the equine lungs. There are three potential solutions to this problem:
1. The equine lungs are non-functional. This seems unsatisfactory, because human lungs alone seem insufficient to provide the amount of oxygen needed by a full-size centaur body.
2. The air reaches the lungs by magical teleportation. This would work, but violates the principle of preferring biological to magical solutions.
3. A centaur's trachea extends down through the human torso, past the liver and stomach, and into the horse torso. Presumably it branches part way down, with one fork going into the human lungs and the other going further down into the horse ones. This seems the best biological solution, although it does mean that the internal organs of a centaur's human torso differ significantly from those of a normal human. Still, we've already accepted that principle when it comes to the brain.
Assuming the third solution is accepted, what this would mean for Dawn is that she'd experience a much greater volume of air passing through her air passages whenever she inhaled or exhaled: it would feel like panting or yawning even when she was breathing normally. I suspect she might need to breathe through her mouth as well as her nose, leading to symptoms of snoring and morning dry-mouth.
Digestion and Diet
A similar problem confronts us when it comes to digestion. The human section has a mouth and oesophagus, a stomach, and probably some of the intestines, but not room for all of them; it has no rectum or anus. The horse section has no mouth or oesophagus, but all the other parts (including some duplicates). Complicating the matter is that humans are omnivores and able to digest meat; horses cannot derive nutrition from meat, but can digest cellulose from plant fibres allowing them to eat grass and hay. We know from Season 8 that Dawn has a craving for hay, so presumably her equine digestive system is able to handle it. Chewing and swallowing would pose greater problems for a human mouth, though I dare say Dawn is resourceful enough to prepare and flavour the hay to make it more palatable. Even as a human she was known for her culinary adventurousness...
As with respiration, the question is: do we posit that the hay teleports from her mouth to her equine stomach; or do we assume a physical connection that it can travel through? If we assume the second, we again have two options. Under one, her oesophagus forks like her trachea, and some food goes into her human stomach while the rest is transported down into her horse stomach. That would require a complex system to determine which stomach the food goes into, either under conscious control or influenced by the taste and smell of the food triggering the appropriate reaction in the brain. There would also need to be a second connection from out of the human stomach bypassing the horse's and feeding into its intestines.
The simpler approach is that the human and horse stomachs are simply connected in series. Food that a human can digest is processed in the human stomach; otherwise it passes straight through there so that the horse's caecum can break down the cellulose. The process would presumably be fairly transparent to the centaur, although she might be more prone to stomach ache and colic than normal. Also, the digestive process as a whole would take longer than it would in either a human or a horse because the food has further to travel.
"Eating like a horse" is a proverbial expression, and because a centaur's body mass is greater, they presumably have to eat even more than that. However, a couple of factors balance this. A centaur's omnivorous digestive system is able to process food with a much higher nutritional value than the grain that makes up a horse's diet, so they need less of it. Secondly, one reason horses eat so frequently is because their stomach is small relative to their size; the addition of a centaur's human stomach also helps to counterbalance this.
In other words, Dawn will probably feel hungry most of the time and feel she's eating like a pig, but she won't actually be eating as much by volume as a horse would. (And certainly less than she did as a giant - but it would probably feel like more because her mouth and throat are now human-sized.)
A centaur would need to consume almost as much liquid per day as a human and a horse combined, due to their body mass. Horses drink between twenty and forty times as much as humans do (40 litres per day) so Dawn will feel constantly thirsty and should rarely be seen without a litre bottle of water in her hand. Of course, all that liquid needs to come out again... something we've also seen mentioned in canon. *g* A centaur's human section cuts off above the point where their kidneys and bladder would be, so these functions have to be handled by the equine organs alone. Assuming the bladder is the same size as a normal horse's, a centaur would therefore need to urinate slightly more often than a horse - perhaps 5% more frequently.
The human torso of a centaur also cuts off above the point where their reproductive organs would be, so these functions are also entirely handled by the horse section. This implies that a centaur's breeding patterns and reproductive cycle are closer to those of a horse; but because their brain is mostly human their behaviour and mating strategies will resemble those of humans.
A female horse goes through an oestrual cycle which repeats every three weeks, as compared to the human 28 day menstrual cycle. Unlike humans the lining of the womb is re-absorbed if fertilisation does not occur, rather than being shed - in other words, centaurs do not get periods. (Since a centaur's arms are too short to reach their genitals, I'm betting this was something Dawn was very glad to discover.)
Another difference from humans is that mares are completely unreceptive sexually for two out of every three weeks: presumably this would be experienced by a sentient being as a total loss of libido and lack of interest in sex. At the end of that time, mares go into heat; a state which is characterised by increased bloodflow to the genitals inducing swelling, increased vaginal lubrication, and other symptoms. These continue for 5 - 7 days. Translating that into human terms, a female centaur is going to feel constantly horny from morning until night for an entire week.
If we assume centaurs are a naturally reproducing species, then presumably one centaur must mate with another centaur to produce a baby centaur. Cross-species mating is a more awkward question. My assumption is that the average centaur would feel as repulsed by the idea of bestiality as a human would be - defining it as "sex with a non-intelligent animal". However, in a centaur's eyes a human and a sentient horse-like being such as a unicorn would presumably be seen on equal terms as potential partners. No offspring could result from such a mating, however. Also, phrasing this as delicately as possible, size would definitely be an issue if it came to PIV sex.
(Dawn's case is different since she used to be human and still has human sensibilities - which explains why she reacts with horror when a unicorn tries to get over-friendly with her. However, since this is a woman who feels quite comfortable going out with a three-eyed Thricewise tentacle monster, I suspect she'd easily adapt if that unicorn turned out to be a nice guy and a great conversationalist after all, once she got to know him.)
When female horses are approached by a stallion, they signal their interest in mating by moving their tail aside and then urinating; when a mare is on heat her urine takes on a distinctive smell, and this attracts the stallion to come over and mount her. Whether centaurs also follow this pattern of mating behaviour is unknown; I suspect that even if natural-born centaurs do take it for granted a human turned into a centaur would be horrified and embarrassed by the very idea.
Horses are known to masturbate by rubbing their genitals against things, so it's reasonable to assume that centaurs can do this too. As previously noted, their arms are too short to reach that area directly. For the record, a female horse does have a clitoris (according to Wikipedia) so presumably is capable of reaching orgasm.
Pregnancy, Birth and Nursing
A horse's pregnancy normally lasts eleven months, followed by a short labour giving birth to a foal which is capable of walking around within hours of birth. A centaur's uterus is presumably the same size as a horse's, and yet a centaur foetus will be much larger than an equine one at the same stage of development because it also has its human torso. Putting these facts together suggests that centaur pregnancies may be shorter than those of a horse - perhaps ten months - but labour will be more difficult. The newborn centaur will also be less developed: it may even be as helpless as a human baby.
A centaur's human torso has a navel; assuming its horse torso does too that implies that an embryonic centaur has two umbilical cords connecting to two separate placentas. In addition, female centaurs have four mammary glands - two human ones and two equine ones (the latter tucked up between the hind legs). Presumably they nurse their baby from all of them, although the equine ones will be less useful until the baby can stand in its own four legs or if another adult centaur supports the baby in place.
A horse is able to lock its leg joints in place by bending its hips in a particular way. This allows it to completely relax its muscles and even sleep whilst standing up. Presumably a centaur can do the same thing; remaining in a standing position indefinitely will not be tiring for them. Note, however, that even a horse must lie down occasionally for a deeper sleep.
Horses, and presumably centaurs, are quite capable of walking backwards, jumping, swimming and lying down.
A horse can gallop at up to 65 kph (40 mph) - some specially bred racehorses are even faster in short bursts. Perhaps not by coincidence, this is also the speed that a Slayer can run at (according to the shooting script of 'Two To Go'). Over a longer distance, speeds of around 15 kph (10 mph) can be sustained for an hour or two. However, horses (and centaurs) are no faster than humans on very long distance treks. Also, note that while a centaur can easily outrun a human, it takes a while for it to coordinate its limbs and get up to speed. Over a very short distance, a human would actually be faster.
A horse requires only two and a half hours of sleep per day, compared to a human's 7 - 8 hours. This sleep is usually obtained in short bursts rather than a continuous period of rest - an adaptation suitable to a herbivorous prey animal. However, I assume that a centaur will require closer to the human level of sleep, since their brains are mostly human - not to mention that they are intelligent omnivores with opposable thumbs and therefore much less vulnerable to sudden attack.
Centaurs appear to be magical creatures rather than demons, assuming such a distinction is valid in the Buffyverse. They almost certainly have souls. Whether they can be turned into vampires is unknown.
So. Any questions?