This part is tricky. And actually gives me an idea on some reading I can do to flesh things out more.
To get things rolling though, I’d assume that monsters operate as a superorganism, like ants, bees, termites, etc. There is an overarching hive mind that determines overall goals, but each monster is an individual. To what extent, I have no idea! yet…
My best guess of how the monsters get bodies, I think there is a genetic soup in the eggs that is activated by this hive mind. Something is sent in, and the body is rapidly assembled. The hard part is, fourth dimensional shapes don’t exactly work in three dimensions. I think this is why some component of each monster is exclusively held within Cherenkov space.
I think it is always easier to reduce dimensions instead of increase them, so for simplicity, imagine trying as a 3D organism to manifest in flatland among hypothetical 2D organisms. How would you even start? Well, I’d make some sort of vehicle that can handle carrying out my intentions and pilot that from outside. I think the monsters are not much different.
This also makes me wonder what happens to humans traveling through Cherenkov space. I will have to do more reading on how 3D shapes handle being in 4D. Hypothetically, there would be an axis of space we have no component in, so to the monsters we’d be kind of like a shadow moving through space. Hard to say. I will have to do research next weekend maybe.
EDIT: as for the nightmares and mind thing, I have no idea - I don’t think being in a higher dimension effects perception of the human mind, but I have no reference to prove or disprove anything in that matter. I’d leave it to pseudoscience! At first it is probably just kala being a drama queen, but that said, they do have full access to her mind via the mutatd compatibility with the hive mind. If monsters didn’t already design themselves for nightmares, they probably will now.