Magical advisers would be weird. They would, at minimum, need to be taken to two-year universities as children to learn Latin and Artes Liberales and given a few years of independent study to learn the different (Realm) Lores. Otherwise, your fief would collapse and explode because crackpot fakers give stupid and utterly false information. Not an unbelievable circumstance, but not one that would prevail long. Higher-ranked nobles would probably want people who attended eight-year universities and the like.
Unless you meant magic-performing advisers? That would be a political mess. The higher-ups would want more powerful ones, but all of them except Elemental Physicians with Refining and Folk Witches would be roughly the same strength because they can't extend their lifespans to learn more. Gifted Hedge Magicians would be the exception, but a Gifted character projected into that position of importance would be given the Join or Die in short order. (Get it? Short order? Order of Hermes? Ugh...) I suppose at the very least there's a potential source of advisers actually being trained by a college in the form of the Learned Magicians of Balogna. But they usually don't have much to do with the (Realm) Lores...
The Order does have exceptionally little contact with mundanes, as a matter of fact. Or at least its wizards do. Or at least they try to.
... Yeah, the knowledge nobles and clergy have of the Order is pretty in-line with what you think it should be. Pretty nod-and-wink all around, though the nobles are a bit less informed than the clergy, with lower-end nobles not having much more than a vague recollection of the fact that Magi aren't allowed to swear fealty to them according to the core rulebook.
The great thing about Ars Magica (I don't know if this was true in previous editions, as I've only played 5th) is how incredible versatile the setting can be for your troupe. This is briefly covered in the later chapters of the Core book, so I don't need to say much, but you can play a lot of different kinds of games with this setting. Pilum of Fire is indeed a very adventurer spell, burning things out of your path and inflicting wounds of varying levels of relevance on monsters. It's not the kind of spell for a politics-heavy or fast-paced game, where you're advancing rapidly, rarely fight or travel much, and/or have very few worthy opponents that you can even fight without getting Marched over it. On the other hand, many troupes like making lots of use of the combat rules and enjoy adventures into the delves of mystical caverns and enchanted forests, especially in slower sagas with younger player Magi. Sagas can have a lot more or a lot less mundane interaction, a lot more or a lot less political interaction with the rest of the Order, a lot more or a lot less combat... And indeed, a lot more or a lot less Mythic.
My own games usually focus a bit more on the Mythic aspects than the Europe aspects, but only like a 70/30% split, not like a 95/5% split. This is simply because my games tend to avoid politics (I play with teenagers) in favor of struggles to overcome more powerful foes, lack of resources, and especially the sometimes chaotic feelings and emotions of the young Magi themselves. There simply isn't room to put in any Europe except for when the characters specifically go to market or meet with nobles. Magic also tends to be a bit more common outside the Order in my games, but not in a good way for society; there are some powerful allies on the side of society, but there's also a lot more hostility against human societies on the part of Supernatural creatures than in most sagas that I've seen others play in, meaning most lower-end fiefs constantly struggle to survive, especially with the amount of corruption I tend to include in the churches that can occasionally result in the lowering of strength of Divine auras until the players fix something. The main reason I don't give the fiefs themselves more access to magical power, of course, is to give the players something to do. That's a really important consideration when tinkering with how you'll run the setting.
The primary antagonists of your story or saga depend on the flavor of the saga. In my games, the main antagonists are powerful beasts and corrupted people in high positions of powers like archbishops and older Magi of the Order. People who you can't immediately open fire against on hunches without serious repercussions, both in them being stronger than you AND the Order's response (have fun getting Marched) but who can generate adventures having their guilt/necessity to be fought proven and whose plots can finally be resolved through generous applications of force. If your saga is supposed to be less combat-oriented, your greatest antagonists may very well be the people who are, according to official records at least, your allies. Say, a covenant of Magi near your own, with somewhat weaker Magi than those of your own covenant but who specialize in certamen and have a lot more political influence and more allies within the Order than your covenant. Suddenly, struggling with them for resources like vis and locations of import becomes a very serious problem that you can't solve with magic and backhanding skills alone no matter how generously or intelligently you apply them.
Magi in games I run, since they're played by teenagers who love action and emotional drama, are a bit different than most Magi, and generally spend a lot of time adventuring, discovering evil plots, and engaging in aforementioned drama. Magi in games I would like to play in if I ever actually had a chance to play this game, though? The exact same thing Magi are generally referred to as doing in the core rulebook. The goal in life of most Magi is, as a general abstraction, to become as knowledgeable and powerful as possible. Some Magi want to become knowledgeable and powerful in different areas, and they might have different reasons for wanting that knowledge and power, like a fear of dying of old age, a desire to lead the Order of Hermes, or what have you. But in the end, the general thing most Magi spend their time doing? They spend their time in their labs, inventing spells, creating items, reading books, studying vis, and for some Magi, adventuring to acquire powerful items or engaging in Order politics in an attempt to become important in the grand scheme. Some do original research to increase the bounds of Magic Theory, some study riddles and try to understand Twilight, some try to bring better relations between the mundane world and the Order of Hermes... They have an excess of possible goals, and most of them are more easily accomplished when you are knowledgeable and powerful. So, yeah. Most Magi do just spend most of their time in their laboratories, learning and becoming better at the things that will push them forward in their largely personal goals.
Hope I've managed to say something useful in this probably unnecessarily long post.
