What do the Inquest do?
A lot of the facilities are tied to personal story missions.
Kudu is merely a high ranking member of the Inquest not the leader. The leader is either Councillor Yahk(confirmed Inquest member) or High Councillor Flax himself(he has the Inquest personality traits and has accused Zojja of sabotaging Kudu).
The Inquest’s goals are enlightenment at any cost.
This is still, years after launch, the best source on the Inquest.
To go through your questions one by one:
*They’re set up as a pyramid structure, and as to their goals: “Gathering information in its pure, crystalline form is their intention, and they will stop at nothing less than the sum of all knowledge. Indeed, the ultimate goal of Inquest research is to achieve control of the Eternal Alchemy, and with it, all of Tyria.”
*Yes. The above article states that the Inquest are organized towards their common goal, even if individual members, and maybe even labs, don’t know how they fit into the bigger picture.
*We don’t know who their leader was, or even if they have a single leader or a council or similar body. It might have been Kudu, since he ran their largest lab, but we’ve never had that confirmed. I don’t think it could possibly be Yahk- when you talk to him, he sounds more like a spokesperson than someone of real consequence. Similarly, I don’t think it’s Flax- he’s ruthless, but it’s been stated that he’s only using the Inquest, and he doesn’t seem to trust them. Either way, though, killing a leader isn’t likely to dissolve such a well-organized entity.
*Speculating here, but I imagine all of their research is at least potentially meaningful. They are still asura, so they’re likely to have their share of dud ideas and deadly mishaps, but they don’t seem wasteful enough to set up a lab in the far corner of the continent without a clear goal in mind.
I like to think they’re just nihilistic researchers, (no price to great for the sake of knowledge), along with the desire to use said knowledge to always be at the top.
I don’t think they have any desire in world domination, though, more than just having the power and knowledge to manipulate the world as they see fit.
As for their structure, no one can make more than just educated guesses, and mine is that every branch operates individually, and there’s some kind of court that regulates the finances between the branches.
I think Kudu was a leader of one such branch, but still has to answer to another entity who decides whether or not his research gets the funds
I won’t repeat answering the questions since Aaron got it all, more or less, but I’d like to add:
Inquest are not evil, they are simply amoral. From the perspective of their victims they are evil, but the main difference is their intent (much like Balthazar).
Kudu, as said was not their leader but simply the leader in their division that focused on Elder Dragon research. One may see Operative Belka as having taken over that field after (though I would be doubtful given her title of “operative”), but who – if anyone – took after after her is unclear. Furthermore, we do not know who the de facto leader of the Inquest is, or even if there is one singular leader (it could be a council for all we know).
As for the last question (“how important is their presence in certain areas”), honestly it feels like the Inquest are just a “go to villain” when ArenaNet needs someone to be a local hostile (which is rather disappointing and overused – can’t we get groups like Modus Sceleris being local villains?), but ultimately all of their research is geared toward the idea of understanding the Eternal Alchemy in some capacity (since all things are part of it). We’ve not really seen “trivial” Inquest labs either – most tend to be geared towards researching dragons, local anomalies (for lack of a better term), or setting up relations with groups that would help with gathering resources or easier access to places they want/need for their research.
Stop treating GW2 as a single story. Each Season and expansion should be their own story.
The Inquest are united not so much by a common goal as a common methodology. Specifically the idea that they should be allowed to do whatever they want to whoever they want in order to complete their research with absolutely no regard for the consequences beyond what they learn and create.
They continued the process of kidnapping sylvari for horrible experiments to learn about their biology long after the rest of the asura recognised them as a sentient (if clearly intellectually inferior) race deserving of ethical treatment.
If they want information someone else has they’re likely to just steal it, or kill them and then steal it (or steal it, frame the other person for having stolen it from them and then kill them).
If an experiment explodes or pollutes the surrounding area or warps the very fabric of reality then…oh well, that’s what happens, at least they got some good data from it.
“Life’s a journey, not a destination.”
You can draw a comparison of Inquest to Google’s (the company) over arching intent of containing and indexing every bit of information there is inside the universe.