Dear Akinbo Ojo,
Wow. You obviously put a lot of thought into this essay and I congratulate you on your effort. I found it very challenging to read partly because I couldn't see the "point" (no disrespect, but pun intended). I realize that it is typical of philosophers to pick a detail such as you did and obsess over it until they have pulled every possible string to its limit, but as an applied physicist, it is hard for me to follow without a clear end in sight.
However, in regards to your hypothesis about time, you said, "Of course, not everybody accepts the cosmological theory, so we are assuming its correctness." Well, in fact, I disagree with the big-bang theory as well as interpretations of singularities as being black holes in spacetime. As I explained in my essay (Doctors of the Ring...) these are mis-perceptions of unified concepts (metaphorically represented by the "golden ring"). If you look at a circle from its side (or as a shadow on Plato's cave) you will see a line. And if there is a particle moving continuously on the ring, the shadow would make it look like an oscillation from one end to the other and back. If you believe that perspective, you will be trapped (under the spell) and won't rise above the plane of opposites to see their unity.
Because the whole cosmological theory is based upon the notion that space is 3D and time is 1D, which is a lop-sided expansion of s = ct, correct mathematics has led to a lop-sided interpretation. It's a foregone conclusion.
I have been working on a model of space-time-motion (which I am about to submit for publication) that represents space and time as conformal projections of motion onto a two-dimensional S-T plane.
*Motion is what is real; it gives matter form. The word motion represents a complementary (unified) concept, i.e. "motion" is a single word used to express complementary antonyms (moving and not moving or at rest); yet the moving state can be expressed in terms of gradable parameters (displacement (s) and clock-time (t)),
*The gradable parameters, s and t numerate (i.e. quantize) and denominate (i.e. reference to standard time scale) the moving state to provide a gradable spectrum by the ratio, v=s/t;
*The speed of light in natural units is simply the state at which the ratio is 1:1
Although I don't follow your logic, I think I agree with your statement that "time is the separator and conferor of discreteness on space". My reason has more to do with the fact that time is the scale that denominates motion, thus giving it a unit magnitude of change. The "curse of Zeno" may be resolved simply by shifting the reference from zero to unity. Any unit of measurement is defined by the "unit", i.e. one unit, not zero. "Zero" represents nothingness so any physically measurable model that includes zero length or displacement, is subject to Zeno's paradox. The concept of time is also subject to the "curse". A unit of time is "measured", although it is not a physical observable, by the motion of a clock (or grains of sand etc). So setting t=0 for analysis of a moving particle means zero relative motion, which is the rest state, so the moving model does not apply.
I hope I made some sense, but it is very difficult to explain. If you are interested, you should read my first draft of the Space-time-motion diagram at http://vixra.org/abs/1402.0045. I have made some changes, mainly to cut down on the philosophy and background material, so check back in a few days to get the latest version.
Oh yes, as for Parmenides philosophy: clearly I disagree with his view that change is impossible, but I agree that existence is timeless because time is nothing more than a scale for eternal (timeless - no beginning and no end) change.