If you're pet feels fine (no vomiting, is active, no blood in stools), then it should be fine. This is mucus and in small amounts is normal. You can give a course of pre- and probiotics and check when was the last time you gave deworming medication.

After neutering cats (and dogs) tend to put some extra weight on. I would have an extra look on the package - are you giving according to the ideal weight. If thats fine and you're not giving extra food (like snacks, treats), then I would check is it a veterinary prescribed food. You can start giving the food from a slow feeder type of a bowl - keeps you're cat little bit more active and she has to hunt her food :). Playing more, trying to get her more moving. Maybe you want to start having walks with her. You're right - overweight trend to dispose to several health problems like diabetes and bladder problems, etc. If this is not working despite of that, then it would be good to check her overall being and taking blood samples.

The pain killers can cause diarrhea (runny stools) and vomiting. If you're pet feels fine (is active, eats well, is drinking, is not vomiting, the wound looks fine) then there is no urgent need to go to the veterinarian. You can give him cooked rice (no added salt) with chicken (without skin). You can additionaly buy stool hardeners which contains kaolin and pectin - you don't need a prescription to buy them. Give him a rice-chicken diet a couple of days and then start giving slowly his cibbles again. If the diarrhea woun't stop in a day then I would discountinue with the pain killers. You should look if he is fine without them. If he is lethargic, feverish, then contact you're vet immidiately.