In America, we hear a lot about Chinese traditional medicine from the medicinal and specifically herbal standpoint. What about its practice? What types of medical specialists were there? How were the different 'levels' educated? Were there midwives? Did they have other responsibilities besides birth? Is there a traditional Chinese gynecology? Did what we would call astrology or magic or religion ever play a part in medical practice?
Yes, I am asking about a broad sweeping time frame to allow Chinese history experts in many eras to chime in if they know the answer, and because I don't know enough about Chinese history to know when the important non-dynastic (so here: intellectual, scientific, perhaps social) changes occurred.
I really want to see someone else respond to the main part of this because I can't except in the vaguest sort of way (medicine was taught something like martial arts with lineages of masters - one of the notable recent ones was Master Ni, who also translated ancient Taoist texts as well as helping to found one of the best known Traditional Chinese Medicine (TCM) universities outside of Asia).
What I can say is that to this day, there's a paradigm problem with TCM because some of its central principles seem to be "what we would call astrology or magic or religion."
Basically, qi (气) is not really quantifiable in any scientific way. There have been attempts to link it to the parasympathetic nervous system (as a kind of network of relations, rather than a "force" or "energy"), and at least one TCM practitioner has tried defining it as an old mistranslation of "oxygen" (much to the chagrin of other practitioners), but students today are still studying texts like the Huangdi Neijing Suwen (the "Yellow Emperor's Internal Classic FAQ" is a rough translation), which is about 1,300-2,000 years old and describes qi as something really like Greek pneuma - an animating force that moves around the body, and can be more or less present in various physical systems.
(For instance, my sister, who studied at Yo San, tells me I have "stagnant liver qi.")
It's not really an energy like light or electricity, and it's not a force that does work. It's more like "vitality," maybe.*
The central paradigm of TCM is based around studying this vitality and the way it moves around the body along certain paths, or "meridians." Acupuncture (or acupressure, or practices like moxibustion) takes place at points along the meridians, stimulating the flow of qi in some places, slowing it down in others.
The meridians are essentially invisible and unmeasurable, too.
Soooo.... because of this paradigm, acupuncture and TCM has a troublesome relationship with science. It fits in just fine with Taoism - especially neidan, the "internal arts" that can include qigong exercises, martial arts like tai chi or bagua, meditation (as described in treatises like The Secret of the Golden Flower) and more esoteric ritual practices. And that body of practices flows right into things we'd recognize as magic - immortality elixirs, levitation, generating heat with your hands, numerology and even correspondences between stars and body parts.
That's not to say it definitively doesn't work - a lot of effects of acupuncture and other qi-based modalities have been measured, and there's an ongoing effort to find out how or why. And in things like herbalism and anatomy, TCM was (and is) really advanced - you might dig the Song Dynasty diagram of organs in this page from the Beijing Digital Museum of TCM. They've got lots of other online exhibits in there - take it like you would any other museum, I guess.
One good source for Chinese medicine basics, besides the translation of the Yellow Emperor's Internal Classic linked above, is Nigel Wiseman's Practical Dictionary of Chinese Medicine.
^* Although in TCM, I think "vitality" is more often a translation of jing, a different concept - more like "pep."