If he is urinating while just sitting there it is 99.99999% chance that it is amedical problem. Could be anything from a urinary tract, kidney or bladder infection or quite possibly a weakend bladder. All of which are easily treated/controled with fairly inexpensive meds. There is a chance it could be a stone or the like, which is a little more involved but still treateable thats for sure.

The diarrhea could be caused from an illness, parasites, allergies, stress, change, etc... the list can go on & on. Has he eaten anything different lately? A change in his food or the like could cause diarrhea as well.

The dragging his bottom on the ground is most likely caused by anal gland problems. Again very easy & inexpensive to get them expressed. Most dogs empty their own anal glands (a little sac on each side of the inside of the anus) when they deficate. But because he's having diarrhea the stool is probably not firm enough to empty them on his own. There is a small chance it could be related to parasites of some sort but again, most of the time when they do this it is caused by their anal glands being full.

The change in behavior is most likely caused by the medical problems he's having but there is a small chance that it could be related to the cats.

I personally reccomend that you make an appointment with your vet. Good luck.