This is a set of follow-up questions regarding this post. The following four queries are very closely related and needed to asked at the same place.
Question 1 Is it really possible to regard the comoving observers to be at rest w.r.t each other even though the physical distance between them is changing with time?
Question 2 Since the double time derivative of the scale factor $a(t)$ i.e., $\ddot{a}\neq 0$, does this mean that the comoving observers are really non-inertial observers?
Question 3 Let us assume that the answer to Question 1 is 'yes' i.e. they can be assumed to be at rest w.r.t each other. Now, when one says that the comoving observers agree on an universal time (assuming synchronized) what kind of choice of time is being referred to here? Is it the proper time observed by any one of them?
Question 4 If the answer to the Question 3 is 'yes', I would ask whether this proper time is synonymous with the term cosmic time (used to define a spacelike hypersurface on which the Universe is homogeneous and isotropic)?