@Floom Great questions. That's a handful to break down, but I'll try my best.
-Ars Magus is basically a form of force created by the fusion of sorcery and science, in its official terms. Nine (Konoe Ayatsuki Mercury) invented it to help humanity against the Black Beast (since sorcery is used in it, it is outside of reason, thus it was able to damage the Beast). Ever since that, a gap between those who can use Ars and those who couldn't, formed.
The problem with Ars is that ordinary humans do not possess the ability to manipulate seithr, the required element, to use Ars, by themselves, and thus, Grimoires are used as "converters" to allow them to do so. Technically, Ars Magus could be used otherwise. It's even stated that everything depends on Magic Formulas (Ars Magus), even the airships work with them.
Burst and Barrier Ars are mainly given to players out of balance reasons, rather than a story-based reasoning, since it wouldn't be fair if they would be always vulnerable to huge combos and unblockable weapon attacks. Plus, I've included them as Ars because Overdrive itself is stated to be "a Magic Formula which helps reduce the burden on the user when they begin using massive abilities" (and Burst and Overdrive share the "Burst Gauge", which implies that Burst is also likely a form of defensive Ars), which also makes me doubt if Ars are a tangible thing at all. Or at least, most of them. As mentioned, we won't be exactly following BlazBlue canon to the letter, since a lot of things are not explained clearly enough.
Also, probably the worst thing regarding Grimoires is that they are not actually "grimoires" in a strict sense : just about anything can become a grimoire, and the why or how wasn't explained in the games, either. As examples, the Azure Grimoire was Ragna's arm, while the Bleu Grimoire is Hazama's body itself. And then there's a grimoire that's "empty" (Pure Grimoire) which looks like a book with a hole in it, and is implied to "gain the power of any grimoire put in it". And it also requires the wielder to be female (turning a would-be male wielder into one if interacted with).
Also also, the creation process of Grimoires, the place Grimoires are kept, and so on, are never shown in the games, either, as far as my knowledge goes... so that's going to be a lot of improvisational work to be done.
Looking at Ars as sort of like "spells" and Grimoires like "spell books" may somewhat simplify the concept of them... until one thinks about how even the airships and the weather stabilizing devices of each Hierarchial City depend on Ars...
-Ars other than the available Burst Ars, Overdrive Ars and Barrier Ars are essentially all under NOL and Sector Seven control, though on a much more limited scale in the latter case, since for one, NOL is the one that basically monopolized Grimoires and Ars, and Kokonoe herself depends on "pure" science instead (she rarely resorts to Ars, if ever). It's only in rare cases that lesser Ars make it out into the public (such as regenerative Ars for certain medicines), and as such, there's not really any other way for accessing higher level Ars and/or Grimoires than being part of either faction, espicially the NOL, and searching for them. Sneaking in or fighting your way in via brute force are also options, though obviously much harder than just being a part of them. And then there's also options of taking down high-level NOL personnel and trying to search them for potential leads or items they may have, but other than that, there's not many options in this regard.
Pretty much the only encountered Ars Armegis will be Tsubaki's Sealed Armament/Weaving Zero : Izayoi (which, due to how it works, is a Tsubaki-exclusive weapon), though depending on how things will go, I may allow creation of custom ones (once again, this
is somewhat of a retcon, after all). In all honesty, I haven't really planned on players dwelling
this deep into terminology and weapon selection
-The "buying Ars from stores" part is also a really good question. Once again, store interactions weren't really shown in BlazBlue, other than at Litchi's clinic (where she
does sell some medicines that use regenerative Ars, though on what principle, once again, a gray area) and at a weapon store in Arakune's Continuum Shift gag scenario, though not much were shown there either. I'd say "no" in this regard, but....
For some reason, it did give me an idea for those part of either faction, or as a secret service from Kokonoe if you do Sector Seven some favors : smelting weapons and items could be an option to "harvest" properties from them in the form of Ars (such as smelting healing medicines to create some regenerative Ars). Letting me your thoughts known on this idea is greatly appreciated.
-I'm pretty sure new Ars are learnt from Grimoires, there aren't really any other ways to learn new ones in-canon. However, as mentioned, humans' main problem is that they cannot manipulate seithr on the level that's required to use Ars without assistance, hence why Grimoires are used as converters to allow them to do so. In essence, learning new Ars happens via Grimoires, but it's possible to cast them even without one if one has a high enough aptitude.
Then again, as we aren't exactly sticking to canon by a hundred percent, I've included certain abilities that function as "Ars", such as Amane's Zettou hop, or Carl's Vivace dash. I don't think that they function via seithr, or like Ars, in-game, but at its core, Ars is essentially seithr manipulation with the assistance of science, and can be pretty much anything (in-canon, confirmed ones include a "cancellation", Mirror's Edge, which created a doppelganger of the target, and Eclipse Barrier, a field which is completely seperated from the rest of the world).
Goodness, I've never thought I'd write such a long reply to a few questions. Apologies for not having been able to give clearer, more concise answers.
@Birthday Feel free to share your thoughts and/or available information in this regard, perhaps you know more about this than I myself do!