I am sorry to hear that your kitten has diarrhea, and has vomited a couple times, but I am very pleased to hear that she is bright playful and active.
Diarrhea in kittens is often due to parasites, eating things that they shouldn't and eating too much table food or treats. Sometimes we do see loose stools in response to food sensitivities, or a sudden change in diet. If you are switching to a different food or from dry to canned food that may be the issue.
Ideally you should have her veterinarian check at least a couple fresh stool samples for parasites as parasite eggs/cysts are shed intermittently and could be part of her trouble. They may be picked up on the second sample or third test if the first is negative. I realize that may not be possible tonight, but parasites are a very common cause of loose stools in kittens so I do recommend that.
Kittens with diarrhea often don't make it to the litter box, and if is a big box that is hard to manage getting in and out that may make it even more difficult. You might try using an old low sided cookie sheet with litter in it placed in the area she has picked to get her used to using a litter box. Eventually you can transition her to a normal litter box, and the area you want her litter box in, but for now just getting her trained to a box is important. The longer she doesn't use a litter box at all the harder it will be to retrain her.
Since she still feels well in general now though we can try some things at home to help with the diarrhea in the meantime.
I would not feed her any food for 6-8 hours.
This should help stop gut spasms and restore normal gut motility.
Small amounts of water given frequently are fine as she needs fluids after all that she has lost with diarrhea. You can give her pedialyte to replace electrolytes too but Gatorade is much too high in sugar which can make her intestinal irritation worse.
Today even with the fast you can start Kao-pectate (or any generic kaolin and pectin formulation) at 1ml per pound or 1 teaspoon per 5 pounds of body weight every 6 to 8 hours. This is quite safe and will coat her irritated gastrointestinal tract as well as absorbing bacterial toxins. You can use it for several days until her stools look normal. You can find kao-pectate at the drug store. If you cannot find the original Kaolin and pectin only formula then skip this step.
After her food fast start a bland diet of 2/3 boiled, white skinless chicken, all fats and juices drained off the meat, mixed with 1/3 boiled, plain white rice. Feed several small meals a day. You might wish to add 1/2 teaspoon of canned pumpkin (not pie filling, just plain pumpkin) to each meal if you are seeing mucous in her stool as fiber helps soothe an irritated colon.
I would add probiotics designed for cats to her bland diet like Fortiflora to rebalance her gut bacteria, as the bacteria population is often off with diarrhea. Other options are Proviable or a probiotic paste called Benebac, which can be used in dogs and cats.
If she has a tense painful abdomen, continues to have loose stools with no improvement after being on kao pectate and probiotics for 24 to 48 hours, becomes very lethargic, begins vomiting consistently or runs a fever greater than 103.5F then she really must be seen by a veterinarian as soon as possible. Make sure to take a fresh stool sample with you when you go.
Once she feels better (no diarrhea for 48 hours) start mixing in her regular cat food very slowly, less bland more regular with each day. It should take a week or so to convert her back.
Most cats can, and should, eat a primarily canned food diet. It may be that the canned food was introduced suddenly or that there is an ingredient that doesn't agree with her. So I would not stop feeding canned food, we may need to try a few to figure out what works for her.
Or her loose stools may not be related to her food, but rather parasites, which is usually the case with kittens.
Don't worry too much about her not drinking much. Canned foods are very high in water content, so she doesn't need to drink much.
Please let me know if you have any further questions.