After looking over several different threads, both here and on the Berkley List, I find myself wondering about my own assumptions. So I am going to write them down, simply to see what they look like, both to my eyes and to others.
First up, I have been playing since 2nd edition, so this colours some of my underlying assumptions (such as the Order being more removed from mundane society than is suggested in the current rules). The primary focus of the game (for me and mine) is on the magi and the development of the covenant.
About 1/3 of the adventures I have run have been combat-oriented -- monster hunts, problems with bandits, problems with martial faeries, a troop or two of knights, and suchlike.
About 1/3 of the adventures have been grog and/or companion oriented, with little to no magical material; some "magical" adventures, due to the players and the day, also ended up primarily as companion or grog adventures.
Covenfolk is a wide category. Most magi have a bodyguard/shield grog, though some forgo this -- about 1/4 of these bodyguards are female; equally many, but not all (usually less than half), magi have a servant. Most shield grogs have significant (Average) arms and armour, though some prefer simpler armaments. For each magus in the covenant there are c. 3 covenfolk. Those who are not bodyguards or servants are involved either in very common crafts (pottery, ropemaking, carpentry, blacksmithing) or agriculture/herding/fishing. Many of the bodyguards also have some other craft or profession, simply because the magi do not tend to need bodyguards 24/7. Most of the covenfolk end up intermarrying. They also tend to speak whatever the local language is, mixed in with small bits of Latin. The covenfolk realize that they are living in a rather odd community, but find there are benefits and keep their peace about this world -- while their material goods may be no greater than those available to other commoners (see below), they tend to have somewhat better health and their efforts are aided through magic, thus producing somewhat larger crops, etc.
There is usually a person (grog or companion) who acts more or less as a bookkeeper/overseer for the covenant, keeping track of mundane stores and the like, including the purchasing of equipment -- this is often a more difficult task than might look at first, as most of these goods are highly specialized and must be purchased from a great distance. Often there is also a library, but not always; conversely, magi are their own scribes -- this is too specialized of a position to attract many others to the covenant and there is not that much extra work for them to do.
Most of the covenfolk are nominally Catholic Christian, though the covenant, due to their nature of attracting odd individuals, there are often other types there as well -- Jews, Muslims, Orthodox Christians, various heretics, and the occassional pagan. Priests, shrines, and churches on the premises are, however, excruciatingly rare.
The covenant itself is at best minimally fortified -- perhaps a squat tower and/or a simple ditch-and-mound defence, possibly augmented by a wooden fence. Much more than this would attract mundane attention. The site is at a fair distance from major mundane communities, both because this is where Magical Auras tend to arise and because this helps to keep a lower profile.
Magi (about 50/50 male and female) are often in correspondence with mundane intellectuals, though this is often done through "blinds" -- assumed names and the like. The magi live somewhat better than the covenfolk (much like well-to-do peasants), but some extra goods.
Many of the (apparent) common assumptions of the Middle Ages are true. There are trolls, goblins, and the evil witches in the woods; vicious animals attack fairly regularly. Toads are poisonous if you handle them. Ghosts often know where piles of treasure are. In general the world is smaller, wilder, and more magical/mystical than our own.
Most of the world is under no particular aura (aka Mundane Aura); those places that do have mystical Auras are notable to most people, if not precisely defined in the same terminology as the Order of Hermes.
As most of 12th/13th century society does not think in terms of money and commerce, the game does not concern itself with this matter either; generic wealth levels are more or less maintained, with only minor opportunities for notable gains or losses in one's economic standing. History is used as a backdrop. It is introduced into the game as it adds to the game itself without interfering with the flow of the game itself. Modern notions of physics, medicine and geography and the like are not included unless necessary.
Well, that is a fair number of basic assumptions. I suppose that will work for now.