They do have a mental connection in some form, it was hinted at in Sol's bio.
but mostly because I wish to remind whatever intelligence that controls this Void incursion that nobody laughs at me in my plane of existence.
Clearly there is some sort of very basic hierachy when it comes to the void. The best analogy I can think of is the Locust from Gears Of War if you've ever played that series. There were many powerful Locust with their own consciousness but the Queen was still in control of all of them and had heavy influence over them as a whole.
Not only that, in this hierachy the lowest level voidborn like the ones u see from Zz'Rot portal and malz have been stated to have very primitive intelligence (Also taken from Sol's bio). How would someone be able to work with Rek'Sai? She just seems to feast on anything when she comes up to surface.
From the epicenter of the corruption, I feel a will… hungry and indomitable, and far from the typical mindlessness I’m accustomed to from these Voidborn aberrations.
So really the only chance of someone allying themselves with the void is to ally themselves with someone who can control the voidborn to not just attack things that are not their own, especially the ones that have very little intelligence. Not only that, the void don't seem to concern themselves with that or any politics. Just seems like destruction and eating are the only things on their mind, i don't think an alliance would really work with someone who has a tunnel vision to destroy and consume the world. You try going to a hungry Lion and ask it if you want to work together...
As for the black mist Mordekaiser has been able to take control of the black mist so powerful figures like Vel Koz and Cho'Gath, I don't see the mist completely subduing them. As for the others, I don't know how much the mist would really negatively affect them. Many of them are just "mindless" creatures who just want to terrorize runeterra so I imagine the mist would just heighten that effect and give them extra powers if anything.