Given that people are now thinking about buying the PDF to get their hands on setting info, looks like I'm writing more fact sections after all. You've already gotten a broad outline of the history, so for this one we'll tackle a bit about 'so how does this Imperium even work, anyway?'
Notes About The Vilani Imperium
Astrography
Galactic directions are traditionally given in terms of coreward (towards the galactic core), rimward (away from the galactic core), spinward (with the direction of the Milky Way's rotation), and trailward (against the direction of the Milky Way's rotation). Typically, coreward is 'north' or towards the top on star maps and trailward is 'east' or to the right.
The Ziru Sirka, or 'Grand Empire of Stars', covers a region of space shaped vaguely like a vertical rectangle that bulges in the middle, stretching approximately 250 parsecs coreward of Terra and 120 parsecs across at its widest point. Terra is located almost directly at the rimward tip or 'bottom' of the Imperium, and the Imperial capital of Vland is almost 200 parsecs coreward of it. There are over ten thousand star systems within the borders of the Imperium but only four thousand of them have major inhabited planets, with slightly over four thousand more of them having outposts (usually for purposes of allowing stopovers and support on a jump-route long enough to require way stations, or resource exploitation or military bases).
As interstellar expansion is limited by the number of viable jump-routes no single part of which covers more than a 2-parsec gap between stars, the vagaries of the starmap mean that quite often you have no direct route from A to B and have to dog-leg around quite a bit. So expansion outward from Vland was anything but even, especially given the navigational difficulties too far coreward.
The nearest provincial capital to Terra is Shulgiasu, seat of the Underking of the Imperial Rim Province (Saarpuhi Kushuggi). Shulgiasu is 11 parsecs from Terra in a straight line, but the jump route to get there requires a long dog-leg to spinward and then back trailward that encompasses 18 jumps in total.
The Terran Confederation is located in a vertical 'corridor' of stars anchored at the rimward end by Procyon and at the coreward end by Nusku. There are no jump-2 routes rimward or trailward of the Terran pocket, and only a few dead-end stars (such as Alpha Centauri) within jump-2 range. All viable jump-2 routes from Nusku lead into Imperial territory. Procyon is at the extreme rimward edge of a slight bulge of Imperial territory, and by traveling 'around the corner' from it you can reach an expanse of unclaimed star systems rimward of the Imperial border. All jump-2 routes from this expansion sector to Terra pass through Procyon.
The Emperor
Technically, the government system of the Vilani Imperium is an absolute monarchy. The Shadow Emperor (commonly referred to merely as the Emperor) or Ishimkarun is the only authority figure in the Empire that can make new laws or repeal laws.
Of course the affairs of so much as a minor polity, let alone the largest known interstellar empire in the galaxy, cannot remotely begin to be managed by a single individual. To the Vilani this is a feature, not a bug. They deal with the Emperor's mortal limitations not by delegation but by precedent - in the absence of a new ruling from the Throne covering a particular situation, the most relevant prior ruling stands. Having started from a carefully engineered system of laws to begin with and then having had 3000+ years of painstakingly gathered and recorded precedents since, this system actually functions; there are very few situations that don't already have a ruling that cannot be at least mostly adapted to deal with the matter at hand and by a lower level of the Imperial bureaucracy. Especially since some rulings actually are of the format 'In situations such as this, official X is allowed to proceed at his discretion... within broad limits Y to Z.'
Obviously this means that the Vilani system is set up to be extremely conservative and with a uniformity of method that reduces the need for different, widely-spread bodies to communicate in order to adequately coordinate their affairs. That was deliberate.
This also means that the single most valuable commodity in Vilani politics is the Emperor's time; if you cannot find a bureaucratic solution to your problem that can be executed by successfully applying prior precedents then you have to get the Emperor to hear you out and sign a permission slip for you to break the rules. Given that there's only so many hours in a day, this means that the Emperor can deliver serious sanctions to any particular department or faction simply by choosing not to pay attention to them, and likewise tip the scales in favor of any faction by picking their latest submission off of the top of his inbox. This is also deliberate, and one of the main sources of the Emperor's authority to begin with. Anybody who tries going their own way without him will rapidly be made vulnerable to the bureaucratic and administrative machinations of every competing faction by the Emperor's simply choosing to ignore them and devote his extra time to facilitating the requests of their rivals, and simple peer pressure will yank them back into line almost immediately.
This also means that the single most important skill for a Vilani official of almost any kind is how good he is at bureaucracy, because their chief and largely only form of dispute resolution short of threats and violence is applied rules lawyering. That was also deliberate.
Obviously of course the Emperor also has conventional sources of authority such as being the commander-in-chief of their military, unlimited powers of high and low justice at his effective whim, and the immense traditional reverence (immense by Vilani standards, a society that already places an extreme weight on tradition and precedent) held for both the legitimacy of his authority and the absolute sacrosanctness of his person. But the first, and usually the only, source of coercion that he has available to use is his ability to pick and choose what he actually pays attention to.
The office of the Shadow Emperor is not hereditary; when the old Emperor passes away a new one is elected the Isgiirdii, the Vilani high council, from among their ranks. Votes are held by open ballot and after each round of voting, the nominee with the lowest number of votes is dropped from the ballot and then another round of voting is begun. Eventually one surviving candidate will hold the majority of the votes, at which point the other candidate drops out and leaves the new Emperor standing alone. One more ceremonial round of voting is always held at this point, so that each new Ishimkarun is officially elected by a unanimous vote.
The Isgiirdi
The Isgiirdi, the high council of the Vilani Imperium, is composed of representatives selected by each branch of the Imperial government via what internal processes that particular branch favors. It's three functions are to propose legislation to the Emperor, to advise the Emperor upon request, and to elect the new Emperor from among their ranks when the old one passes away. There are 300 total delegates but only fifteen of them hold the office of 'Speaker'- one each for the Army and the Navy, three apiece for each of the three great shangarim (more on these later), and four at-large Speakers selected by the Emperor.
The office of Speaker is important because legally, they are the only members of the Isgiirdi actually allowed to talk to the Emperor at all. (And now you know why he's formally called the 'Shadow Emperor' - he's not a public figure.) Everybody else in the Imperium has to go through one of the Speakers in order to petition the Throne. The Emperor is of course allowed to be in contact with anyone he wishes, but that's a case of "Don't call him, he'll call you."
The Imperial Government
Although it has aristocratic ranks and dynastic houses for the purpose of ensuring long-term continuity, functionally the Imperial government is a corporate bureaucracy.
The three Shangarim, or "bureaus", are three huge agencies that collectively manage virtually all of the day-to-day operations of the Imperial government. They each ultimately descend from a power group among early Vilani society - the aristocrats, the shugili or what was effectively the old priestly caste, or the industrialists. Each of these bureaus both has direct administrative control of a portion of Imperial territory and bureaucratic authority over all activities within their bureau's broad specialty anywhere in the Empire.
Yes, this mixed control means that there's a tremendous amount of bureaucratic cooperation - or infighting - to get anything done on a large scale at all. That was also deliberate. (In fact, there's very little about the Vilani system of government that is not deliberate; they have spent millenia of effort socially engineering and fine-tuning this thing, and it shows.)
The section of Vilani space that encompasses the entire Imperial Rim Province and thus is the one ultimately dealing with the Terran problem is underneath the territorial supervision of Sharurshid, the Vilani bureau whose primary Imperium-wide bailiwick is shipping, commerce, and industry. Makhidkarun is the bureau whose bailiwick encompasses the administrative functions normally thought of as government functions - police, media, education, etc. Naasirka is the bureau whose function covers the 'basics of life' - largely food and energy production and distribution.
The Imperial Hierarchy
Parallel to the multiple interlocked bureaucracies of the three great Shangarim is the official Imperial 'noble' hierarchy, each member of which (save the Emperor) is a hereditary dynast of one of the great clans that traditionally compose the senior management ranks of one or another of the Shangarim. Usually, an Imperial noble in a given territory will be from a family of the same bureau that has been assigned that territory as a fief, but not always. An attempt to wrest the office of the Apkallu Kibrat Arban away from the Sharrikun family of the Sharurshid bureau and claim it for one of the ruling families of a rival bureau is the affair that so distracted Shana Likushan away from the Second Interstellar War.
Starting from the top - the Emperor - and stepping one rank down we have the twelve "Great Ministers of the Four Quarters", or Apkallu Kibrat Arban. These titles are traditionally reserved for leaders of the three great shangarim and their most trusted and senior subordinates. Each of these nobles supervises the activities of 2-4 sectors of the 14 or so sectors that collectively comprise the Vilani Imperium.
The next rank below them is that of Underking, or Saarpuhi, each of which supervises approximately 80-150 separate worlds, a number that usuallly comprises a significant chunk of a single sector. Simple astrography means that the Saarpuhi Kushuggi, the Underking of the Imperial Rim Province facing Terra, operates on a somewhat looser leash and with more discretion than a Saarpuhi in one of the Imperial core sectors would.
Beneath the Saarpuhi are the ranks of the 'supreme governors' or Sarriiu who typically oversee subsectors with a dozen or so inhabited worlds apiece, and 'provincial governors' or shakkanakhu who occupy a flexible level of the bureaucracy that can end up overseeing anywhere between one and half a dozen worlds as needs require.
Each of these titles, save that of Emperor, is hereditary - but with a twist. A Vilani noble title cannot be inherited by the first or secondborn child of the prior occupant of the title, but must be granted to a third or lower-born child. The first two children are still members of the executive or 'noble' class, but are expected to show merit, work their way up the bureaucracy, and find other suitable high offices to be appointed to. Furthermore, adoption for the purpose of gaining an heir is not permitted under any circumstances.
This is, of course, deliberate. It's intended to ensure that there is a slow but regular turnover of lower-ranking titles to new families as old ones fail to have a large enough number of heirs and leave the titles vacant for reassignment, as well as ensuring that any particular family dynasty spreads out in each generation to make new connections. This fosters more complex and multifaceted webs of obligation and prevents any one great family from permanently consolidating too much power.
Beneath the aforementioned hereditary are the equivalent of Life Peers in Terran aristocratic nomenclature, non-hereditary noble ranks assigned at need that fill out the management ranks of the entire Imperial government bureaucracy. Some of these ranks, such as the high admirals and generals of the Imperium, are in practice wielding more seniority and prestige than all but the highest of the hereditary nobles despite being life titles.
Of note is that Vilani lifespans tend to run almost 150% of Terran lifespans due to certain variances in their evolution, which has a certain steadying effect of its own on the rate of social change and dynastic turnover.
Subject Races
Approximately 10% of the total population of the Imperium are non-Vilani humans of other offshoot races, and another 10% are nonhuman sapient races. Very few of them had star travel before the Imperium assimilated them, and even the largest and most advanced interstellar polity - the Vegans - still only controlled somewhat over a dozen worlds.
The Vilani treat their subject races with a mix of naked imperialism and generous inclusiveness. So long as a subject race shows even a moderate tendency to wish to conform to Vilani culture and government, they are treated identically under law as any other Imperial subjects. Obviously the hereditary and conservative nature of the higher ranks of the Imperial government means that subject races (human and otherwise) have very little direct representation there, but Vilani rule tends to be no less benevolently oppressive to conquered peoples than it is to their own population. Only the most incorrigible resisters have their worlds still under trade interdiction or forcible military occupation.
On the other hand, a subject world that doesn't want to follow Vilani law and culture is going to get pressured until it does, even if they have to use sledgehammers. The only exceptions that begin to made are for races nonhuman enough in their psychology that the Vilani have to settle for just having them conform to their legal and bureaucratic system and let their culture handle itself.
This legal equality combined with uncompromising cultural imperialism means that the Vilani have been having to deal with occasional uprisings and local unrest for about as long as the Imperium has existed. Given the immense advantages of size that the Imperium has against any single world, this is seen as no more than an inevitable but minor problem caused by quirks of sophont nature that would be impossible to engineer out of a population and are simply dealt with if and when they occur.
Of particular note are the Anakundu, a human strain that was one of the earlier races assimilated into the Imperium. Having been only at a Neolithic level of development when the Vilani made first contact, pretty much their entire culture and industry is the result of Vilani uplift. They are nigh-invariably strong Imperial loyalists and are one of the very few non-Vilani races to occasionally hold high positions in the Vilani government.
The current Saarpuhi Kushuggi of the Imperial Rim Province, Sharik Yangila, is an Anakundu.