Boy these are hard questions. Action by standard physics is the integral of energy difference, the lagrangian, over either time or space or spacetime. Time and space are therefore implicit in action and are just another way to keep track of action.
We can count the spin periods of an electron as a sequence of actions, which is what we do and we call that counting time. That is how time emerges from action and likewise space emerges from the charge radius of the electron. We know that matter is a part of the universe and how matter distributes affects action and so we also like to keep track of matter. The charge radius is an intrinsic measure that allows us to keep track of matter as space or volume. That is how space emerges from matter and action.
This approach gets rid of all of the pesky infinities that plague space and time. Any 1/r2 force has a singularity at r=0 and the indivisibility of space is a tough nut to crack. In an discrete aether universe of discrete action, the problems of space and time are simply artifacts.
Rational and irrational numbers are a way that we keep track of space and time because for discrete aether and action, whole numbers are all that one needs. However, carrying around 1e39th digits is real silly since most action only needs a percent or so of precision for prediction. So we carry around a convenient number system that helps us predict action.
In the aether universe, all energy and momentum are equivalent to mass changes just like for all matter-energy equivalence. Therefore aether is fully compatible with relativity's MEE, but aether does not really have event horizons or light cones. The decay of the universe is what defines the speed of light and that means that all event horizons are where they belong in defining the edge of the universe.
This does mean that as matter decays, force and the speed of light increase, but that simply is the way the universe works. The galaxy red shift is real but due mostly to the slow speed of light in the early universe and therefore the weak charge and gravity forces as well...but there was more matter in the early universe.
The units for time and space are both dimensionless counts of spin periods and charge radii. We then assign those dimensions any convenient metric just like we do with wavefunctions, which are also dimensionless.