The Progenitors are humans and the Kushan are their descendantsThe latter bit is actually pretty well-hinted within the backstory of the second game and stated outright in earlier versions of the game's script. The former bit on the other hand is pure conjecture. However, since it's been known for some time know that the Homeworld galaxy is modeled after M51 (aka, the Whirpool Galaxy) and it's been stated that the Progenitors originated from a different galaxy originally, then, assuming that the Homeworld galaxy actually is M51 (rather than simply resembling it) then it isn't too much of a logical leap to assume that the Progenitors came from the Milky Way, colonized the Homeworld galaxy, and then declined to more primitive levels, becoming the Kushan (who, as of Homeworld 2, canonically look exactly like humans).
The Naggarok was a Progenitor far jump prototypeSort of related to the above, it's possible, given the Progenitors' extragalactic origin and mastery of hyperspace travel that they are the same race that designed the Naggarok - which was explicitly a hyperspace test vehicle for long-range jumps and which originated from outside the Homeworld galaxy. Of course, one might point out that the Naggarok is several times older (about a million years old) than even the oldest Progenitor relics in the Homeworld galaxy (about a few hundred thousand years old). However, since the Progenitors arrived after the Naggarok launched, its possible that, after working out the pesky Beast infection problems of traversing intergalactic hyperspace, the Progenitors colonized the Homeworld galaxy a few hundred thousand years later.
The Kadeshi joined the Kushan to repopulate HiigaraIn Homeworld 2 the Hiigaran population is twenty times the number of initial Kushan settlers. So, how did they manage to multiply so much? One possibility is that the Kadeshi provided a population boost: they could have tried and chased the Kushan in the attempt to stop them before they alerted the Taiidan, only to find a space station and dozens of Taiidan ships destroyed on their path, and reached them at Hiigara, finding out it was now safe and free. Somehow, I think they'd prefer to return home... And by the time of Cataclysm the Taiidan Imperialists feel safe at going into the Kadesh Nebula. The Kadeshi must be somewhere else...
The Homeworld universe is the far future of Known SpaceThe Progenitors were humans and/or protectors fleeing the irradiated Milky Way, and the three long jump hyperspace cores are Quantum II hyperdrives. This also explains why all of the seen races of Homeworld are Human Aliens - they are humans.