Hello, my name is***** and I have over 20 years of experience as a veterinarian.
I'm so sorry to hear that your kitten Gus has intermittent diarrhea, frequent stools, and is urinating outside the box.
Short term diarrhea can be stress related but it rarely lasts more than a few days.
In a young cat with diarrhea that seems to feel well otherwise I would be highly suspicious of gastrointestinal parasites or a food intolerance. Sometimes we can see bacteria overgrowth leading to diarrhea too.
I know that his stool has been checked once for parasites but parasite eggs/cysts are shed intermittently, so it may take several stool sample checks to diagnose a parasite in some cases. I also know that he has been wormed, but not all parasites are worms (some are protozoa) and no wormer covers all parasites. Your veterinarian needs to look for protozoal parasites (like giardia, coccidia or tritrichomonas), and abnormal bacteria, as well as the usual worms. So I highly recommend that a fresh fecal sample be submitted to the lab rather than checking it in the clinic as these can be hard to find, and sometimes we need to check samples from several days in a row to find them. Metronidazole is an antibiotic that is also an anti-inflammatory so it works well on an irritated intestine. That is a medication we often prescribe for kittens with nonspecific diarrhea.
I will often treat them for parasites while I wait for test results with broad spectrum worm medications like Fenbendazole (Panacur) when loose stools linger.
I am glad that he is on a probiotic like Fortiflora to try to replace normal gut bacteria. Another option is Proviable. Probiotics should be continued because cats with chronic loose stools almost always need their gut bacteria rebalanced.
At home now you can try a couple things.
I would not feed him any food for 12 hours. This should help stop gut spasms and restore normal gut motility. Small amounts of water or clear broths like low salt chicken broth given frequently are fine as he needs fluids after all that he has lost with diarrhea. You can give him pedialyte to replace electrolytes too but Gatorade is much too high in sugar which can make his intestinal irritation worse.
Today even with the fast you can start Kao-pectate at 1ml per pound or 1/2 teaspoon per 2-3 pounds of body weight every 6 to 8 hours. This is quite safe and will coat his irritated gastrointestinal tract as well as absorbing bacterial toxins. You can use it for several days until his stools look normal. You can find kao-pectate at the drug store.
After his food fast start a bland diet of 2/3 boiled white skinless chicken, all fats and juices drained off mixed with 1/3 boiled, plain white rice. Feed several small meals a day. You might wish to add 1 tablespoon of canned pumpkin to each meal if you are seeing mucous in his stool as fiber helps soothe an irritated colon.
Once he feels better (no diarrhea for 48 hours) start mixing in what will be his regular kitten food very slowly, less bland more regular with each day. It should take a week or so to convert him back to regular kitten food.
It is possible that Gus's loose stools come on quickly, and he doesn't have time to make it to his box. Confining him to a small area when he cannot be directly supervised until he is feeling better and has normal stools should help. It is also possible that he has some cramping with his loose stools and he is starting to associate discomfort with his box, and thus doesn't go there hoping not to feel the discomfort. Hopefully as he feels better that will change.
Urinating outside the box may be an indication that he is a kitty that likes to urinate in one place and defecate in another. Two litter boxes in different places may help that. He may also have a surface preference for cloth to urinate on. Don't give him the option for that to happen by picking up towels promptly and confining him to an area with his litter boxes and away from towels/rugs until he is using his litter box consistently. Vinegar does not adequately remove the scent of urine. You must use an enzymatic cleaner to remove the scent. Nature's Miracle is one that works well. Here's a link that shows their products: http://www.natures-miracle.com/products/pet-odor-stain-removers.aspx
Best of luck with your little one.
Please let me know if you have any further questions.