Should a diaphragmatic hernia be operated on even if it is small in an adult?

No: Hiatal hernias are so common as to be nearly a normal finding. Unless it is a paraesophageal hernia keep the knives in a drawer.

Depends: A small hernia could be an asymptomatic event ration. Depends on how the diagnosis was made. If symptomatic it should be addressed, usually with surgery. Oftentimes it can be done minimally invasive with laparoscopy.