Comoving system of expanding or collapsing dust-like particles

I have a question on comoving and synchronized reference systems. I read the corresponding section (97) on Landau/Lifshitz's second book field theory on it. In particular it is said that space filling matter cannot be in rest in such a system except in case of dust-like matter with pressure $$p=0$$. This is the case I am interested in. Because further on in section 103 of Landau/Lifshitz a solution of Einstein's field equations (EFE) is discussed with just this assumption. Would an observer in such a system observe that all surrounding particles collapsing to a single point in rest with respect to him?

I also seem to have an example of matter moving a comoving synchronized system. A Robertson-Walker metric seems to describe a comoving synchronized system of the cosmic matter in the universe. If cosmic matter would not move WRT such a system, how would it be possible to notice the expansion of the universe ? So if matter does move in such a comoving system, what distinguishes it from a simple rest frame of single chosen particle (participating in an expansion of collapse) whereas the other particles of the matter distribution move with respect to it ? Is a comoving synchronized system a special case of a simple rest frame and if yes in which respect?