Do you have the sourcebook? That will help with some things. Also try searching the Blue Room archives: http://www.tekumel.com/blueroom.html
Also, you should buy Deeds of the Ever-Glorious. It's a huge collection of legion histories. It's especially useful in your case for the Pe Choi and Pachi Lei. Hardcover from Tita's House of Games or you can buy a pdf file from DriveThruRPG.com
Some other bits and pieces:
--The Temple of the Flame (Vimuhla and His Cohort) is the most influential temple in the city, so it certainly is somewhat militaristic. However, many of the Red clans of the west (Red Mountain, Red Stone, etc.) have kindred across the border in Mu'ugalavya that they maintain recurrent trade and social ties with. So militaristic yes, but not ready to burn down all the Red Hat towns...
--The Pachi Lei hate the Mu'ugalavyani, and have good reason. The Red Hats seem to consider PL subhuman, and when they have invaded or controlled Pan Chaka (2020 A.S. and during the recent Civil War), they attempted to exterminate the Pachi Lei there, and did great harm. The Petal Throne has two legions of Pachi Lei, one each for Stability and Change, and despite their religious differences, both would dearly love to fight the Mu'ugs. They have in the past fought the Itos too, but never the Pe Choi. A Pe Choi legion once rescued the first Pachi Lei legion when both were serving against the Salarvyani, and the Pachi Lei still sometimes refer to the Pe Choi as "our northern forest brothers." There are however many different communities of Pachi Lei. Some isolated deep in the jungles of southern Pan Chaka, some more "civilized" (or "humanized" around Butrus, and some in cities across Tsolyanu, very much part of human society. There is probably a sizable Pachi Lei community in Tumissa.
--The Ito clan is a powerful and ancient group of humans who have lived in Do Chaka since time out of mind. They are very old-time Sarku-worshippers, and have very high status. The Itos, like the Vriddi in Fasiltum, have historically been reluctant subordinates to any empire, and have occasionally rebelled against Imperial rule, often playing one empire off against the other.. Iirc, they were somewhat reluctant backers of Prince Dhich'unÃ©. They are not a big presence in Tumissa or (I think) any other large city. Their strongholds seem to be back in the hills...
--The Pe Choi in the Chakas are politically and religiously divided. There are Pe Choi legions in the armies of both adjacent empires (4 for Tsolyanu, 2 I think for Mu'ugalavya), and there are "wild" Pe Choi who serve neither and occasionally raid either or both. There are rumors of an ancient pre-Collapse Pe Choi city somewhere deep in their enclave.
--During the recent Tsolyani Civil War, the Mu'ugalavyani invaded. They took Butrus and Pan Chaka, and besieged Tumissa, but couldn't not capture it. There's not much canonical information about the military and political events in the west and southwest during the war.
oh, also, join the tekumel yahoogroup and download the tekfiles from the Misc. section of the file archive. There are lots of personalities in there.
hope this helps. Tell us more specifics about what kind of game you want to run (high politics? gritty combat? underworld delving? social scheming? what status level?) and we can probably add more useful stuff.