A fairly common trope in fantasy is "barbie doll anatomy". Effectively, a species completely lacks any visible orifices besides their mouth and nose. This brings up two major questions. First, how would such a species reproduce, and second, how would it deal with waste in the body? Since these races are so often magical, an answer involving magic is fine. Thanks!
Inspired by the natural world around us, here are some weird but real options:
Certain animals have a transient anus. This is a bit of a frame challenge but still, you can walk around with no visible opening for 99% of the time without anyone noticing anything.
A lot of snail species use "love darts" that literally wound the other snail during mating. Although these darts aren't the thing that transfers the sperm, there is no reason why in your world this couldn't be the case.
As for gestation, this is tricky. There are (were) however frogs that do "gastric brooding", i.e. they incubate their young in their stomach and then...well, throw up their offspring.
Admittedly though, none of these options really has that Barbie vibe.
Ant larvae do not excrete any waste material. They keep their excrement contained until they grow into pupae.
When ants are in their pupal state the waste collects in a sealed little plug at the end of the cocoon. It's a dark spot. Then when the cocoon is shed it can be thrown away.
(Having worked with ants, it's a very tidy system and seems to keep their nests clean as they raise the young.)
So a Barbie organism could molt, and simply have a dark spot of concentrated waste that would be removed when molting. (Here is a fascinating article on ant poop lol: https://www.pestcontrolgurus.com/ant-poop/)
No visible orifices
Many great answers already, but I see one avenue not considered in detail. All it takes is for the orifices to not be visible. We could have a feather or fur cover that retracts and be fine. With reproductive organs and waste organs actually not needing any length, only good positioning, you're basically done.
I recognise that this isn't really the spirit of the question. Barbie dolls are without fur, feathers or other covering and any clothes can be removed for orifice inspection. Let's see options that would suffice for an inspection on an uncovered body.
Holding an orifice so tight it looks like smooth skin seems a bit of a cop out, so I'll skip that.
Reproductive organs do not actually have to get inside another. Though this is the most common practice, we can see several other kinds. Think of eggs, or simply pressing two holes close to each other for transfer. Penetration has it's advantages, but it does not rule out this kind of reproduction. So covering them up and only opening at required times would be enough.
As mentioned in another question, the anus can form when needed. This can then be applied to any orifices. The easiest implementation is to have all the internal plumbing in the 'normal' places, but with a layer over the orifice. It'll be dissolved or ruptured when it is required to function. Skin grows too slow, so maybe something similar to blood clotting, or a substance that is excreted and when exposed to the air/drying out will form a layer that looks like skin. If it's anti bacterial all the better.
Sadly barbie is lacking a belly button and other not normally orifices, or else it could do tripple duty as a not obvious orifice.
We can hide the orifices in unusual places still. We can hide it under the feet, a place we normally do not inspect closely. Again, we can inspect it on a doll, but assuming a 'real' barbie it might not be realised until much later. Do not ask what leg they use for reproduction if no third leg is available.
Perspiration. Absolutely everything... They might need to drink copious amounts and also wash rather often... Still waste material could be remove by glands around the body.
For reproduction egg laying like certain species of fish would do. Females lay eggs and then male lay sperm. Both could come from organ in or near head and be relatively small. Growth cycle from that point is somewhat open. Potential lactation for feeding could happen by some type of mucus. Mixing this process with the waste removal is likely not preferred.
Magic could help these processes by lowering food requirements and supplying the energy for growth to certain limit.
A species with only one orifice has two options, 1) magic: waste is removed magically, it just disappears by magic. And it's a similar story with reproduction, insemination happens by magic with sperm magically appearing in the female body and the baby also appears by magic after growing inside its mother's body it magically appears outside of her body 2) the one orifice is used for all functions: this which would be rather unpleasant, but is physically possible even if it's biologically very questionable.
They are plant or fungus based
The visible orifices on a human are the mouth for eating and tasting, the nose for breathing and smelling, the ears for hearing, the anus for pooping, and the sex specific orifices for urinating and reproduction. While mammals generally work this way, there are plenty of macro-organisms here on Earth that don't have any of these orifices in thier bodies, but they are pretty much all plants and fungi
When you eliminate the need to eat other organisms, suddenly the need for giant holes to consume food with becomes unnecessary. Plants and fungi don't have mouths. Plants consume most of thier energy through photosynthesis, and get most of thier chemical building blocks directly from the air and water The vast majority of organic chemistry only uses hydrogen, oxygen, carbon, and nitrogen; so, even trace amounts of other stuff is all planets really need the soil for. Fungi, similarly use a sedentary method of absorbing nutrients. Even though they eat other organisms like animals do, they don't consume them. The excrete digestive fluids onto thier food and sit on it while they uptake just the nutrients. If you never take in what you don't need, you never have anything you need to poop out.
Breathing holes are also not exclusively necessary. Plants, fungi, and many amphibians breath through microscopic pores in thier "skins". So, it's highly feasible that a fantasy race could breath through thier skin too.
Hearing does not require holes. While mammals tend to have orifice based hearing organs, we are actually the exception to the rule. Reptiles, mammals, fish, and amphibians can all hear just fine without any orifices.
Like the mouth, your anus and urethra only exist because we eat other organisms whole, then have to sort out what we do and don't need and expel the unneeded stuff. If you ate more like a fungus or a plant, you'd have time to sort things out before you eat it, meaning you don't need a massive excrement system. What little waste you might need to worry about could be excreted like sweat.
Lastly, there is reproduction. Again, most plants and fungi don't pernitrate each other's orifices to reproduce. Some us a form of buddy where a part of the body just falls off and becomes a little clone of the parent. Other use purely external sexual reproduction methods involving pollination and fruiting.
So, as long as your barbie-folk get to spend long hours rooted in the soil, and basking in the sun, or spend thier nights sleeping in a big pile of food and self-excreted digestive fluids, then major orifices could be unnecessary.
Reproduction with magic
- The mother cuts a very small bit of her own flesh
- The father cuts himself and adds a few drops of his own blood on the mother's flesh
- They add some water from the ancestral river
- Then they join hands and cast a magic spell on the mix of flesh,blood and water.
After the fourth step, the mix of flesh,blood and water turns into a gelatinous egg with a fetus/larvae inside.
If the parents are interrupted before the fourth step, before casting the magic spell, then the mix of flesh,blood and water will still turn into an egg with a fetus/larvae inside, but it will not have a soul. It will have the body of a Zora and be able to breathe, but will have no soul, no mind, it will just be an empty shell. (Ignore this paragraph if you don't like it)
To keep it more grounded to the real-life inspiration, your creatures do not need to eat or secrete waste, and they reproduce by casting plastic on a mold they made lovingly for the purpose, as part of a ritual which casts the animating magic on the new being. They're all animated by magic rather then having anything resembling a real-world metabolism.
Many birds do not excrete waste matter. Instead, indigestable matter remaining in the stomach is regurgitated as a solid pellet. Owls and hawks are best known for this, but other birds do too.
The bird still passes urine though, but the hole for this can be very small. Especially if your species has fur, feathers or scales, you're never going to see it.
This is most unusual and an unique feature of her physiology. Now, human hair is made of a matrix of proteins giving it strength and suppleness (not to mention gleam from the oils in the scalp).
"Barbie's" hair is composed of a complex polymer made from urea (the primary constituent of urine next to water) and complex carbohydrates (usually present in stool as roughage). Her gut of course is remarkably efficient in breaking everything down as it should and water normally present in urine is conserved, except a normal amount of sweat with salts present.
She has to be very careful to regulate her diet, but can chose to change her skin and hair colour to suite her surroundings and social expectations by altering what she eats. Her remarkable abilities extend to laying on curves, altering her facial appearance to have East-Asian, Afro-Caribbean, Caucasian or mixed features at will.
When the time comes, having detachable limbs that snake-off on their own to find food and grow serves well. We all know the subject of Barbie's innocence, but if there's a "Ken" (or another Barbie) who's limbs decide to entwine in that special way, then an offspring will develop.
Unnecessary genetic material is shunted aside and reabsorbed, perhaps during a cocoon-stage then a youngling emerges of an appropriate gender. (Whatever the writer decides that may be) Limited parental care is needed, no breastfeeding as the baby will find its own meals.
Of course, a new limb quickly grows to fulfil the deficit in the parents' limb count.
Eating is obvious, the mouth serves just fine - the same for respiration and speech. (and kissing?)