No. Fibromyalgia is a pain disorder in which pressure on specific points produces pain and pressure on adjacent points does not.
No. The symptom constellation is diverse and heavily ladened with psychologic disarray, unhappiness, and outright depression. Within the practice of medicine there is an unfortunate tendency to ascribe, to the mind, complex symptoms for which there are no tests of proof. "hypochondria" is nowadays a term little used, but the concept continues to shadow "fibromyalgia" in the minds of some doctors.
Criteria exist. There are published diagnostic criteria for the diagnosis of fibromyalgia. First, other similar conditions must be ruled out, then the diagnosis is confirmed through exam by a physician familiar with fibromyalgia. You must have at least 11 of 18 defined tender points, pain >3-6 months, pain above & below waist, pain on both left & right sides of the body, as well as other associated symptoms.