If they haven't put him on dialysis and the kidney has already failed, the odds are that he won't need to go on the machine at all. You only need to go on dialysis if both kidneys have failed. The dietitian in the hospital will tell him what is good for him to eat,but there should be no special restrictions. He will most likely have to keep hydrated, but again they will tell him what to do.
You are right about the pillow for coughing. While it is a large surgery,I know many people that end up leaving the hospital in about a week. It does take a month or two to completely recover, as I said before, but usually people live just fine with only one kidney.