What sort of political parties exist within the Egyptian Senate? Do we only have one house of representation, or two?
The senate is bicameral. The party system is... ill-defined at best; traditionally there are the monarchists who seek to increase royal power and those who currently oppose them; a large part of the Senate can swing either way, though.
And also, do our elites speak a Norman version of French, or what? How egalitarian is Egyptian society?
The current "Aegyptian" language has evolved from a combination of the Norman dialect, Latin and Coptic, with generous helpings of Greek and Arabic. The
elite, however, speaks Latin, or so is the tradition (ofcourse, nowadays it is bilingual, but supposed to known both Latin and Literature Aegyptian).
-What exactly were the circumstances surrounding the aforementioned coup d'etat? The one a few decades ago.
Hmm? A failed military takeover, of a sorts; a conspiracy involving the commander of the Fulda garrison, some of his fellow officers and the more radical and opportunistic Arbeitist circles; they were planning something like a more radical version of the OTL February Revolution, but failed to secure the support of most other generals or the Reichstag. There still was an armed popular uprising in Fulda itself; it and the garrison's attempted treason had to be put down by force, leading to some brutal, bloody and well-documented fighting in the streets that helped put the contemporary Imperial government's prestige in the gutter.
-Following the suppression of the Bohemian revolt, what exactly is the situation vis-a-vis Czech national rights? Are they appropriately downtrodden and exploited?
Czechs? What Czechs? You surely mean "Upper Elbe Germans".
In other words, see modern Kurds in Turkey. Ofcourse, the majority population in Prague is German or so Germanised as to be largely unaffected by the national revival; some of them tried to reclaim their Slavness during the uprising and became subject of amusing stories written by this world's distant equivalent of Hašek.
-If the Reichstag is elected via the device of universal manhood suffrage from the entire Empire (save the colonies?) what function do the Kreise fill?
They evolved over time, and became something more like military/higher-level administrative districts.
-Is there any von Tirpitzian or even Gorshkovian figure, a German Naval League, anything like that? Or has the fleet managed to stay unpoliticized so far?
No, the fleet has never been important/"The Reich has two allies: the German army and the Flemish fleet" (though there is a German fleet as well; it's just not much to speak of).
-In our eastern territories, what's the ethnic distribution? Who lives where, and how many of 'em?
Other than Bohemia and maybe Posen, all those areas have majority German populations; Livs and Estonians are still a significant presence in Ostland, as are "Eastern Danes", whereas the Posen area, eastern Pomerania and especially Prussia have large Polish populations.
-Any noticeable linguistic differences in German compared to OTL? What's the distribution of the dialects (if there are any), and what are they like?
Well, ofcourse there are major differences (or, rather, lots and lots of minor differences) and there fairly noteworthy local accents; without going into too much detail, let's say that Bavarian is much less the odd one out, unlike "Pomeranian" (Pomerania in the broader sense includes OTL Brandenburg and nearby areas in this case).
-Philosophically...well, uh, where are we? What happened?
See my answer to Thlayli.
I have some basic cultural ideas here and there, but it's pretty incoherent as of now, and the specifics are probably best left to the players anyway; but the overall theme would be much stronger continuity with High Medieval civilisation in its various aspects (despite a genuine, undeniable and significant evolution since then), plus closer and earlier contacts with India and traditions thereof. There exists a great emphasis on social order in European thought, but just what it is and how it is to be achieved is argued a lot, with aristocratic traditionalists on one end, middle class pragmatic reformists on another and radical reformist-to-utopian revolutionary Arbeitists on the third end, if you want a Hearts of Iron-style triangle of political practice and philosophy.
You are having wayyy too much fun with this.
What's monarchy without amusing over-the-top scandals?
What is the status of abolition around the world?
Mostly done in name except some places where slavery was never a huge factor in the first place. In reality some colonies have been using slavery-in-all-but-in-name, and in some cases reliance on slave labour is increasing rather than decreasing.
Is there any regionalism within Arcadia akin to OTL states rights in the United States?
Nothing remotely comparable to
that, in Arcadia Proper. The greatest source of regionalism would be the British Isles by far.
Are the domestic affairs of the British Isles and Arcadia proper completely divorced from one another in governance?
Nearly so, but most domestic governance tends to be devolved to local authorities in the first place; the supreme authority in the British Isles is the royally-appointed governor-general who reins akin to the monarch himself, though is kept under control, in parts due to fairly regular rotation.
Are the instruments of government generally the same as their OTL British equivalents?
Similar in general, but the Parliament is so much weaker and less developed; it's probably similar to the 1760s parliament in most regards.
What are the major Arcadian political parties?
Re: Arcadian party system: see Egypt, but more divided, less stable and more confusing and chaotic. There are some "Imperial-style" political parties
now, but most of them are bickering variations on parliamentary liberalism and are predicted to be likely to fall apart and recombine several times over the next two decades, while the York party (devoted monarchists with an occasional pragmatic streak and the most stable party, though it is not very large and could usually be outnumbered by a liberal coalition if such a thing was physically possible) looks on and
laughs.
What about New Albion? What political organization does the corrupt republic have?
The Assembly of the Republic and the President thereof. Real power belongs to various urban bosses and vested interests, though.
When did the Anglican-Catholic split happen? Was it before or after the sharding of the British Empire?
Already answered. Just after/during/it was a part of the process.
How prevalent and autonomous are Amerindian populations outside of Oklahoma?
Not very and usually rather yes.
How does the Japanese population compare to the native and Arcadian/English/whatever populations in the Japanese colonies?
In the coastal cities it is probably more or less a majority. The English remain in some coastal areas. The inlands are largely populated by natives and English metis groups; the latter are increasingly numerous. Note that the population as such is still largely concentrated in coastal areas and the cities specifically, and though no proper census has been conducted despite some attempts, the Japanese probably still have a (uncomfortable) majority for now.
I hate my countrymen. 
