Well, that is really quit a list of complaints, but let me try to answer your specific question. A headache specialist is anyone who lists their primary practice as headache - they could be a neurologist, internist, family physician etc. They may or maynot have completed a fellowship training program in headache. The neurologist deals with neurologic disease and one of those is headache. Again they may or may not be trained to deal specifically with headache.
Most neurologists treat headache but few specialize in it.
The pain care center staff varies and usually includes a number of different specialties. Often you see an anesthesiologist, a neurologist or internist, a psychologist etc. The MRA will not rule in or out basilar migraine. I think they are doing it because of the prolonged spell that you had they wish to make sure your basilar artery does not show and abnormality that may be causing your problem. Basilar migraine involves a specific symptom complex that can be very frightening.