I have classes in a bit, so I'll be dipping out for a while. I'll answer any stockpiled answers when I return.
It still boggles my mind that people see having to read through things like the provided snippet as an upside.
...In hindsight, maybe I should've picked a different snippet. Or just stuck to the first paragraph. ^^;
Assuming it's not too much trouble (like if detailed notes don't exist yet), who are some of the big names in LH, and what magic do they use?
Rebecca Croce utilizes the magic "
Foxfire," and has the same as one of her titles. Fire is not actually involved at any point; instead, illusions and vivid hallucinations serve to render her foes vulnerable to the ancient and powerful spell known as "Fist." She's more interested in the development side of things than the archeology end.
Alecco Gori is a user of Shadow Dragon Slayer magic, or what amounts to consuming shadows for power, controlling them, and
becoming them. He frequently uses his ability to pass through blocked or unstable areas too small for a full-sized human to fit in.
Oza Nieri utilizes a variant on Take Over magic with a name not known outside the Guild. Take Over magic usually requires personal observation (and frequently damaging the target) in order to assume traits from a given creature. Oza instead manages to target now-extinct species and assume their traits, including traits from titanic dinosaurs and multiple powerful magical creatures hunted to extinction.
Has anyone within the Guild dabbled with Warlock magics post-legalization?
Over a sixth of them have done so just to see how it interacts with their preexisting magic. Most of them didn't pursue it beyond that, but a couple have continued to study what would be classified as Warlock magic now that they're allowed to do so. The Lost Magics in question are still pretty close to as they found them, though.
I don't really want to ignore the difference in stigma - yes, it's mostly about sacrifice, but... if they don't have a warlock they might assume our kind of magic is going to lead to that eventually. And Blake is already worried about that, so reinforcing that with external stigma means we're less likely to be able to develop useful skills that might involve sacrificial magic? If you put Blake in a guild with people who have fears or apprehensions about her magic that could make her afraid of her own powers later on, or at least having to consciously work to avoid fairly standard Black effects like paying a little life up front for things.
As an aside, any concerns would be less from societal hesitation and more from their experience with things like "sacrificial spells that used a city as fuel."
[
Also keep in mind that picking Angel's Eye wouldn't be the only possible source of companionship for Blake—and yes, Blake could form friendships within Liquid Horizon. More preexisting friendships and social groups—and less emphasis on an environment intended to foster close friendships among everyone in the Guild—just means it'd be trickier. "New member!" is a big deal in Angel's Eye due to their size; not so much for LH. Both MGLN and RWBY also have their fair share of groups that would accept her (although it'd be much harder for Blake in RWBY, so maybe I shouldn't include that as a point

).
It's also worth remembering that Liquid Horizon specializes in archeology
and the development of Lost Magics uncovered from those expeditions. Plenty of members don't get involved with ruin-delving at all.
*lights match*
Liquid Horizon would also have more leads on the possible locations of Gold Celestial Spirit Gate keys, or powerful objects which essentially follow "input mana, receive a specific powerful warrior (one per key) willing to assist summoner." I will confirm they are capable of summoning the intelligent entities linked to them across planes. (EDIT: And it's pretty likely that Blake would become friends with them.)