Is obesity an eating disorder?

Yes, Maybe, and No. Its the consequance of decision to eat more than necessary.
No. Obesity is a physical condition that may result from many factors, including poor eating habits, heredity and culture. Some people do not know what’s healthy and eat meals high in calories/fat. Others are genetically prone to being at a heavier weight or don't get enough exercise. Binge eating disorder is a complex psychological condition in which people use eating to resolve internal conflicts.
Not nesessarily, metabolism varies, but it can be cured by eating less. You might be hypothyroid and benefit from thyroid medication.
Yes, Maybe, and No. Whether obesity is an eating disorder depends on whose definition one uses, and on what odd behaviors occur. A binge eater who eats huge amounts in an hour has an eating disorder. A chocolate addict who got obese on 3 lbs of chocolate a day has an eating disorder and an addiction problem. A person who got obese by eating a normal dessert 3 times a day for 20 years doesn't have an eating disorder.