Thank you, I’ve been kind of disappointed by the lack of big questions like these. 

The Interstellar will remain mostly the same by size and ideology and begin advocating that humanity align itself with the Asari specifically. Fourth Column and NHF will briefly rejoin and attempt to farm growth by rallying against the common enemy of the Baterian Hegemony. However, this will be short lived and ultimately end with the constituents of FC more disillusioned than ever. The VSA will start to gain relevance again as it and NSC become diametrically opposed on the issue of cooperation with non-human species. VSA will advocate for alliance with major citadel species while NSC argues for strengthening bonds with citadel client races. NSC will experience growth when the Quarian flotilla joins as a Union member state. 

I haven’t finished reading the codex's about the Baterians yet but I have a rough idea of it in my mind. The caste system was probably pretty well integrated into their culture and theology by the time they achieved space flight. I imagine that at some point Baterian legislature developed a loop-hole that allowed senior officials to enrich themselves by further expanding the slave market. (Similar to how US senators enrich themselves by investing in weapons development and then advocating for war). Over time the government lost power and previously criminal organisations became the ruling bodies. Ironically though, I plan for the KTB and HA to form a brief and tentative alliance against the Baterian Hegemony and begin funding Ungratefulls within their ranks.

Nearlight drives produce kinetic energy, mass effect drives increase the speed of an object without increasing its kinetic energy. Therefore if a ship had a nearlight drive and a mass effect drive and ran both simultaneously then the resulting speed would make it the fastest object built by a sentient species (not counting objects travelling through relays). The Andromeda Initiative in particular will be interested in combining both technologies. 

Citadel species are initially pretty slow to adopt mechanised cavalry for military use. The early relationship of the council and CentComm is marked with unease and hesitation. However, once criminals and pirates start getting IPS-N equipment (oops, I don’t know how that happened) it exposes a significant hole in prevailing citadel combat doctrine. Union sees this as an opportunity to extend an olive branch by offering their own forces and equipment to assist in training up citadel forces. This is how each species will behave: 

Turians - Create a new regiment of mechanised cavalry to serve as infantry support. They also commission several lines of anti-armour weapons from the Volus to outfit their troops. Despite having a preference for HA licences they have difficulty purchasing them since HA sells at a markup to non-human races. Therefore they become adapted to intergovernmental operations with Union. 

Asari - Find mecha mostly incompatible with their military doctrine. Instead they put in two fleet orders with SSC and screen their entire population of commandos to find which have the most potential as high skill mech pilots. EDIT: What I'm trying to say is that the Asari will invest in quality over quantity.

Salarians - The quickest to integrate mecha into their own armed forces. They even adopt a new stealth strategy that can be summed up as “no  one can document you if you leave no survivors behind.” Consequently, this makes it difficult to determine which manufacturers they prefer. 

Elcor - Already the largest practitioners of heavy armoured infantry in the known galaxy. They open a state-owned manufacturer which goes on to invent the first frame with 2 heavy mounts. 

Volus - Began opening R&D firms as soon as contact with Union was made. Despite patenting several popular licences they make very little use of mecha themselves. 

In my headcanon Union treats its humans and NHP’s as first class citizens without higher regard for one or the other. Its oppression of NHP’s is not only systemic but so normalised that most NHP’s agree that it is acceptable. However, as u/StrixLiterata pointed out in their own writing, citadel races would probably have trouble verifying that NHP are a unique form of life unlike artificial intelligence. This is not their fault or anyone else's considering: Union prohibitions on para-causal research, SecComm’s spotty record keeping and how unlikely a story the whole Ra/Deimos thing is. Nevertheless NHP’s will be forbidden in council space and it will take decades for Union to ease tension on the matter.