Is diarrhea considered to be a communicable disease?

It depends. Diarrhea is not a disease but a symptoms. Many of the diseases which cause diarrhea are communicable (viral diseases, hepatitis a, clostridium difficile, salmonella, etch). Most causes of chronic diarrhea, however, are not communicable.
Possibly. There are many causes of diarrhea. Diarrhea caused by infections with viruses, bacteria or parasites should be considered communicable.