Meh, as usual, Japanese barely put effort into properly using other languages. It's like really crap google translate with getting wrong letters all over the place.
When Krasnyi, Seenii and Rozavyi mind link they become one mind with three bodies and they have each other's abilities, so each body gets three of them (long range, short range, support).
"Belyi" is a self-aware entity born from this mind merging, or so it claims.
When "they" say to be one person acting on its own, that's Belyi talking.
To put it in simpler terms, there's four minds here - Krasnyi, Seenii, Rozavyi, and the fourth one which is made up by the former three linking together into a single being.
Belyi is not always doing the puppeteering, it said so itself that it would arouse suspicion. At the end of the chapter when the three amigos are in bed, that's Rozavyi acting on her own (might be these three never saw anything but snowy Siberia their whole lives).
Them having lewd and sloppy threesomes though? That's Belyi enjoying itself, at least to an extent (does it count as selfcest? the bodies are different, but the mind is not).
Weird that the assignment of abilities to categories are:
Close Range -> Spatial Detection
Long Range -> Body Enhancement
Search -> Brain Wave Enhancement
Something like this would make more sense:
Close Range -> Body Enhancement
Long Range -> Brain Wave Enhancement
Search -> Spatial Detection