United Empire is my favorite faction in ES2. Mostly because of their music and militaristic tendency, but I am also an admirer of Zelevas. He is brutal and unforgiving but polite and charming (in my opinion). One thing I have not been able to figure out, perhaps due to my inexperience in the field of psychology, is whether he is an evil psychopath or simply a pragmatic, doing what is in his people's best interests without moral consideration. From what I have seen of him through the UE questline, I am leaning toward the latter, but am still unsure.

From lore in ES1 and ES2, we can make some assumptions. He was the CEO of a massive mining corp before he became emperor, and is implied to run the UE as a corporation. He allows certain groups more freedom than others, such as the sheredyn. His goal is to gain as much power as possible. Check the wikis for more info, but Id say its somewhere in between evil and practical, as corporatism and elitism is allowed to run free.

Can you tell me how much power he wields within the Empire? Is he like an absolute monarch or does he have to share power with the Empire's business heads?

Pretty sure he's an absolute monarch, but he manages the empire as a whole. Organizations, families, or corporations within the empire are allowed the deal with the small details. The empire is incredibly large, so national identity varies greatly. So greatly in fact, that 2 factions (there may be more I just don't remember) split off from it, being the Sheredyn, and the Pilgrims (With the pilgrims being a sort of religious group, feel free to look them up). The Sheredyn didn't really split off, but are what sounds like the most powerful group within the empire, assigned as the personal guards of the Emperor. They were essentially just a personal army that got so large they needed to make infrastructure to support themselves, but that infrastructure just so happens to now make up a big chunk of the Empire as a whole. I would suggest reading both

https://endlessspace.fandom.com/wiki/United_Empire

and

https://endlessspace.fandom.com/wiki/Sheredyn

I'd say it depends on when in the campaign you ask. He consolidates the power as the missions go on, but starts with a quite feudal system early on, imo, where his subjects wield a lot of power themselves.

And, to be honest, the beauty of the ES2 is that whether he's a dangerous sociopath or not depends on how you play as UE. How many planets have you destroyed lately? ;)

B- but Endless Space 1 lore

One more thing Cobbs. How does the Emperor ensure that the sheredyn remain loyal? If they are the most powerful group in the Empire and the Emperor is an absolute monarch, isn't there massive danger that they might take over?

I'm not quite sure. In the Endless Space 1 wiki, it says that the Emperor took power, it was done with the complete approval of the Sheredyn. To directly quote the wiki,

This was in complete opposition to the traditional stance of the organization; it had always pledged loyalty to the emperor regardless of questions of "right" or "wrong". Arguments can be made in favor of the Sheredyn's actions, however. Zelevas was the CEO of a wide-ranging conglomerate, XenoMine Corp., and widely acknowledged as a genius as well as an inspirational leader. It helped, of course, that the reigning Emperor Willema Szinda had gone from honest and energetic to senile and unbalanced. Still, this shift in Sheredyn loyalties was unthinkable to many.

This was in complete opposition to the traditional stance of the organization; it had always pledged loyalty to the emperor regardless of questions of "right" or "wrong". Arguments can be made in favor of the Sheredyn's actions, however. Zelevas was the CEO of a wide-ranging conglomerate, XenoMine Corp., and widely acknowledged as a genius as well as an inspirational leader. It helped, of course, that the reigning Emperor Willema Szinda had gone from honest and energetic to senile and unbalanced. Still, this shift in Sheredyn loyalties was unthinkable to many.

It says in other sections that Zelevas has greatly extended their Autonomy and the extent to what they can get away with. Zelevas utilizes the Sheredyn to project his power, but the Sheredyn allow him to reign because of the autonomy he gives them? So in short, the Sheredyn exist to protect and assist the emperor, but the previous Emperor was really bad at their job, and Zelevas was looking like a pretty good candidate, so they assisted him in gaining enough power to overtake the previous Emperor. Now, Zelevas uses them to project his rule, and in exchange grants them the power to essentially just be an autonomous state within the empire.

(Sorry if I was repetitive, I'm tired, and I'm learning more as I write)

Is the Endless Space 1 lore still valid in 2, though? The quest line says that he essentially came out on top of a war that lead to the actual (re?)unification of the empire. 

Well both the Sheredyn and United Empire exist within ES2, and I assume that their origins have stayed the same unless otherwise stated