Ok. First of Relic doesn't own the licensing to the Homeworld franchise but THQ does. This means that likely Homeworld 3 is coming. Relic and THQ have never had a mod pulled and I wouldn't find it surprising if they encouraged making this mod or at least not object to it.
Anyway, echo-apollo kind of glossed over the races. Here is a time line for reference: http://homeworld.wikia.com/wiki/Timeline
The Kushan and Hiigarans are one of the same. They were once a great empire that fell after they did naughty things and made the Bentusi take there core away

. They were exiled to Kharak before they returned to the Higgara (which caused the Tiiadan Empire, which were there old arch nemesis, to fall) and grew before the fight with the Vayger, which they barely won.
The Taiidan were another Empire that formed around the same time has the Hiigaran's created there own. They entered a a war with them which ended in there favor. The empire had already started to collapse before the Exile's return, but it was the finial nail in the coffin. Out sprang the Taiidan republic from Cataclysm made of revolutionaries, but in Homeworld 2 there not even mentioned.
Kadesh are a relitivly minor race. They lived in a rose pink nebula and were decendent from the exiles. They called the nebula the Catherdral of Kadesh and attacked any "heritic" that enterd and refused to join.
The Vagyr are a nomadic group of pepole that lived on the outer borders of the galaxy. They were united by the Warlord Manikan who almost conquered the Hiigaran's new empire in a crusade. He is defeated with the help of Sajuuk.
The Bentusi used to be the galactic UN peace keeping force. However they fell from the position after the galaxy revolted. There last aggressive act was the defeat of the Hiigarn's first empire and then the exile. After that they chose to be completely peaceful and became nomadic traders, "unbound", directly connected to there U shaped trade ships. Bentus is the Harbor ship. It holds the Bentusi's core until it exploded to save the Pride of Hiigara from attacking Keepers. It is worth noting that it is said that Bentus is the last of the Bentusi. If Cataclysm is to be taken as cannon then it would be possible that they are not dead but merely not within the galaxy the game's take place in. I doubt they would be in this mod if its during/after the Vayger Crusade.
T-mat this is wannon. I am unsure exactly what these are. However:
"T-Mat: An ancient race of technologically advanced nomads who travel about the galaxy completely stripping star systems of all usable matter, energy, and biomass to sustatin their considerable consumptive needs. Though not overtly belligerent, the ruthlessness of T-Mat resource consumption, and their uncaring attitude towards the devastating effects of their practices, has resulted in their being feared throughout the galaxy. The appearance of a T-Mat mothership is ones space is rarely a good omen."
— Dust Wars documents
Progenitors the creators and created all the new races. They built He Who's Hands Shape What Is aka Sajuuk, plus of bunch of other things like the megaliths and Keepers. They are all dead now (Keepers are robotic) and it is never made clear how they died.
Turanic Raiders. Think SoaSE pirates. That pretty much explains them.