Those are great questions! My favorite thing about Carcosa is Shub-Niggurath and its spawn.
Following are some notes regarding the six regular spawn of Shub-Niggurath and how they differ from Lovecraft's descriptions.
Primordial Ones: Their mighty civilization is long, long gone. All that remains are ruins and scattered artifacts. The Primordial Ones that currently exist on Carcosa are in small bands of 1-10, a majority of them without the benefit of high-tech. They hold all other intelligent life in utter contempt. They think everything should be their slaves. They especially hate the Shoggoths. Unlike Lovecraft's version, Primordial Ones on Carcosa are psionic.
Shoggoths: Lovecraft was pretty vague about these things. They obviously are incapable of forming a civilization. They utterly hate the Primordial Ones. Shoggoths will occasionally cooperate with Deep Ones, but other than that do not like the other regular spawn.
Mi-Go: Lovecraft's Mi-Go are brilliant scientists. Not so Carcosa's. They have an average I. Q. score of about 70. They never established a civilization, instead having a level of culture similar to that of cavemen. They are psionic, however. They do not interact with the other five main spawn.
The Great Race: Like the Primordial Ones, the mighty civilization of the Great Race is long gone. Only ruins and scattered artifacts remain. The remaining members of the Great Race live in small groups of 1-12, and they only rarely have high-tech. They tend to avoid the other main spawn.
The Deep Ones: These are about 50% Lovecraftian and about 50% Kuo-Toa. Lovecraft's Deep Ones lived in cities found only on ocean shelves. Carcosa's live throughout the ocean, as well as in damp caverns. Lovecraft's Deep Ones lived in mighty cities. Those on Carcosa live in small communities of no more than 100. Also, Lovecraft's Deep Ones could wipe-out humanity if they cared to. Carcosa's Deep Ones (like the Kuo-Toa) are a race in steep decline. They avoid the other main spawn of Shub-Niggurath, except for occasionally employing Shoggoths. Some particularly degenerate groups will even worship a Shoggoth.
When Deep Ones interact with humans, contact is minimal. You'll never find a Deep One in a pub, for example. The Deep Ones interact with humans only to spread the cult of the Old Ones (expecially of Cthulhu) and (less often) to interbreed with human women. Such women are sometimes outright raped, and other times pressured into it by their society. Some of the most jaded and perverse of women, bored with human males, actually welcome the exotic embraces of the Deep Ones. In any case, there is no question of "relationships" between the Deep Ones and human women. It's just sex. The Deep Ones flap from their lairs, do the deed, and then slink back.
B'yakhee: These are a creation of August Derleth, and I don't remember them being anything other than magic transports that come at the call of a whistle. In any case, they never formed civilizations. They are fanatically loyal servants of Hastur, and will certainly not come like a dog to a whistle. They serve humans only when it furthers Hastur's goals, or when forced by sorcery to do so. They are psionic. They are aloof from the other six main spawn.
In short, the only interaction between any of the six main spawn is between Deep Ones and Shoggoths, and that is rather rare. None of them are numerous or widely influential. They are all well past their heydays. Eventual extinction seems their lot.
The Primordial Ones used to conduct big biological experiments. Undoubtedly these experiments created the semi-intelligent humanoid snakes that later (after the destruction of the civilization of the Primordial Ones) evolved into the
Snake-Men.
The Primordial Ones also undoubtedly created the man-apes from which the races of
humans were much later bred by the Snake-Men.
I hope all this answers your questions, bluskreem. Of course, all the above is true only of my own Carcosa campaign. Your (and others') Carcosa campaign might very well differ.