An anesthetist is a person who gives a patient medication (usually in the form of gas) during surgery and other major medical procedures to either render them unconscious or numb to pain.
Yes, you can receive anesthiologists' services at the Yale-New Haven Hospital, but normally this requires getting surgery at the same time.
4 year college+4 year medical school+4 year intern+1 or two year specialization in a certain area
Probably a bunch. Anethesialogists are resposible for knocking people out for just the right amount of time. If you give someone too little drug, they could wake up early, compromising an operation. If you give them too much drug, it could cause permanent, even fatal harm. And calculating the amount of drug required for a given person would require math.