Do fentanyl patches cause stomach or intestinal bleeding?

Not really. Side effects of narcotics include slowing of the intestinal tract and constipation, commonly, but not damage to the lining of the intestines. Non-steroidal antiinflammatories such as ibuprofen, aspirin, naproxen, etc., & even steroids, however, are notorious for causing intestinal bleeding. If you develop intestinal bleeding for any reason, see your doctor immediately. It could be life-threatening.
Very unlikely. As it is not oral and opioids in general do not cause GI bleeding it would would be unlikely.