Baller, after we do the nations, we might have to go after independant towns :p
First I'm going to add to what you've already said.
Their colours are blue and black (should we make flags for these nations?), and I believe that the triumvirate is advised by more philosopers than military advisors, which may make them formidible adversaries in global campaigns for their unconventional tactics, or make them weak foes due to their higher ups making novice mistakes. I'm leaning more towards the former.
I can see them being friendliest with the Guild, while constantly battling with the Republic.
-The Guild represents structure, everything for the allmighty currency (What is the currency in this world anyway?), making them predictable, as well as alleviating pressure fom the League by constantly warring with it.
-I agree that the Empire is old foes with the Baronies, but are separated by the desert, and thus rarely see conflict on their borders.
-I would think that their relationship with the Order would be pleasant, but they might be warry of them; they're a nation with strong scientific background, and may not be easily converted. Also, the Order's philanthropic tendancies might make the Empire suspicious, believing that the Order is playing the same game as them.
-The general populaiton of the Arashi would see the Empire as being exactly the same as the Guild. The leaders of the Arashi see through this; although they prefer the Empire to the Guild, they don't believe that "The Better Way" would be any better for them, in fact they see it as being worse, as they would probably have to pay tithe to the Empire regularly, while still living in an inhospitiable desert, as well as loosing (guessing) a third of their income from scavenging and raiding.
-The Angleans....the Empire reeeeeeeeally hates. Barbarians, isolationists, raiders, they spit in the face of everything that the Empire stands for. It wouldn't be so bad if they wern't right on their doorstep! The southern Republic towns constntly raid the northern coast by ways other than the usual trade routes, mostly raiding for food and luxury goods, but not adverse to taking thralls. In response to this, I can see the Empire building "Enlightenment Institutions", or something similarly sinister sounding, just for Anglens. These are little more than hard labor camps with terrible conditions for raiders and those who will not immediately convert.
China is pretty diverse, but (thanks wikipedia) 92% of the population is of the Han ethnic group, and they pretty much just speak one language, Mandarin (I've yet to meet a mainlander who can speak Cantonese, which is sad since I'm part Cantonese). Of the other 8%, I've heard there are about 50 minority ethnic groups. There are local dialects, and some words are noticibly different depending on where you go (In the north, the word for 10 and 4 are distinctly different to my ears, sounding like "Shuh" and "Seu", but on the middle all the way to the coast, 10 and 4 sound the same in spoken language by the locals, "Seu"). In any case, I hope the Yeshan Empire is a bit more diverse, it would be neat and a pain in the butt to have to learn different languages.
I can see the Empire really hating anything that opposes their idea that their way isn't the right way, using very drastic measures, especially if those that oppose their ideals are Yeshan themselves. They would have to be, to keep a diverse population from splitting into independant nations.
Also: I LOVE that joke!