I think blood tests could be worthwhile and a sample of his stools being analysed. It could be an infection. Obviously through the diarrhea ensure he is taking ample liquids to prevent dehydration. I think he should see the Doctor about this as quickly as possible.
I can't comment on the bowel problem, stress and a reaction to drugs come to mind. The dry cough I'm betting is a result of the medication(s) he is taking, a normal side affect of ACE inhibitors. I had the dry cough for a couple of months after my first heart attack, but the body gets used to the drugs, and they do help the heart heal.
Do correspond your concerns to your father's doctor.