Easy to get confused. Gluten-sensitive enteropathy (celiac disease) is much less common than gluten intolerance. Like lactose intolerance, caffeine intolerance, sorbitol intolerance (with regard to needing to restrict each respective substance), people who are gluten intolerant do better to avoid gluten-containing foods. Only about 10% of the population are gluten intolerant--an inflammatory condition of small bowel.
YES. Very rare less than 5% of the population has it and needs a Gluten Free Diet to cure the Symptoms. The rest of the Gluten Free faddists blame Gluten for everything from migraines to hemmorhoids.
Kind of. It is under category of "digestive" diseases (i.e gastroenterology), but it is not a problem with digestion but rather a problem with absorption of nutrients.