Is your risk of infection (from various causes) increased by a very unhealthy diet?
Sure thing, it's like driving your car with no oil, stuff starts to go bad fast. Fill your gas tank with old gas-bad news. Eat right, exercise, take care of yourself, see the doc. regularly & you'll most likely live a long healthy life.
Yes. An unhealthy diet can affect your immune system which in turn makes infections more likely and more difficult to fight off.