I have a two and half months female kitten for 3 days. She doesn't enjoy dry food so far so she's eating primarily wet food - from can or pouches, but I started mixing them with dry food. I think her intake of water is normal - she's drinking some time after her meal or after she's tired of playing. What concerns me is that I've never seen her peeing - she's only popping. Her poo is rather watery and soft than solid, but I'm hoping that this is due to the fact she doesn't eat dry food. Is this normal? I'm planning to visit a vet for vacation next week, but I'm a bit worried at the moment.
To start, any time a cat is not urinating, it's urgent to get them to a vet ASAP. While urinary issues typically affect older (and neutered male) cats, any cat can suffer urinary tract issues which can become serious to fatal, and even less serious cases can result in long-term behavioral issues, such as litterbox avoidance.
Secondarily, it sounds as though your cat has some digestive issues as well; watery or soft poo is not normal, and should be addressed by a vet ASAP. It may be an illness, parasites, or a sensitivity to one or more foods you're offering; the vet will be able to run tests on a sample of the poo to determine if an infection or parasite is present. He or she will also be able to offer advice based on the food you're offering.
And thirdly, dry food is not necessary. It's convenient with kittens, as they need to eat a lot, but offers very little benefit other than convenience. Cats typically do not consume enough water on its own, as they originated in desert climates and are adapted to get their water from food; wet food offers hydration in a manner more natural to them. A healthy cat fed an all-wet food diet (with any ingredient sensitivities accounted for) will produce normally formed, firm waste; the water is absorbed from the food during digestion.
If her poo is watery, that’s why: her body isn’t absorbing enough of the water in her food, leaving her too dehydrated to pee. This is a serious concern since peeing is how the body gets rid of non-food waste, and being dehydrated in general can cause kidney problems. You need to take her to a vet, which is a good practice anyway when you get a new pet.
Are you feeding her the exact same food (brand and flavor) as whoever you got her from? A sudden change in diet can cause short-term digestive distress while the gut bacteria adapt, which will be exacerbated by the stress of a new home. This will solve itself in time, but it’s still better to stick with what her body is used to at first. Once she’s stable, you can then slowly switch her to what you want to feed her long-term over a week or two.
The other major possibility is some sort of infection or parasite. Unfortunately, kittens often pick up worms or other diseases in shelters or catteries because that many animals in close proximity means they’re constantly passing them back and forth, making them virtually impossible to eradicate. Your vet will do a fecal test to check for these.
Cats are pretty much able to abstain from pee and/or poo out of stress for a few days. Not that it is good for them, but they do.
There is also a possibility that the pee happens in a place(s) other than it is supposed to. If an adult cat does so, the smell is inevitable, but little kittens can get away for a while.
There is also a possibility of some restriction in the urinal tract - pretty low probability in a small female kitten (older male ones are the ones suffering usually). The symptom is the cat trying to pee for a minute or two with little or no success.
You can try to touch the cat's bladder by fingers. It is undetectable under the skin in a healthy cat, but feels like an inflated ball if the cat cannot pee for one reason or another. If there is a ball, see vet immediately (failing to feel the ball does not guarantee anything and you may want to go to vets anyway).