Now we are rocking...I like how you enumerate your arguments...
"1. When matter is not separated, we have one. That is, if there is nothing between two bodies of matter, we have one body of matter. But we have many bodies of matter in the universe, therefore what separates them, which is space, is not nothing."
When you say separated, you are already assuming space exists a priori. Time is what separates objects, not space. As long as time separates two objects, they will also be separate in their projection back into space given some action.
"2. Talking cosmologically, if there was therefore nothing at the beginning, even space must be absent."
The of course, space would not be the lonely empty nothing that it seems to be...and you would have invented another nothing, maybe a multiverse or a supernatural agent? Look, all we can know is what is in this universe and while we can ask what exists outside of the universe, there is no way to answer that question. We ask and answer these kinds of questions all of the time, but that is the realm of belief. Although science starts with belief in axioms just like religion and philosophy have their axioms, the axioms of science reflect the limits to what we can know.
"3. Which is more fundamental, matter or space? Can you have matter without space or can you have space without matter?"
The answer for me is easy. Matter. But you cannot have matter without time and action and it is with the action of matter in time that space occurs.
"4. If Einstein's E =mc2 is correct and the measure of matter is kilogram, then the kilogram is not an ultimately conserved quantity."
In my cosmology, that is correct. In fact, matter decays as exactly 0.283 ppb/yr and it is that decay that determines gravity and quantum action. Correspondingly, c increases by the same fraction each year and so our measure of atomic time gets another second every 65 years or so.
"5. To further apprehend the nature of space, it should be discovered if it is infinitely divisible. If it is not, then it is not a nothing but a different kind of something."
This is easy for me since space is whatever convenient thing you want it to be. Space is not needed to predict action, space is not needed to separate objects, and space is not needed for the matter exchanges that determine all force.
"6. From 3,4 and 5, perhaps we replace matter with space in the triad, so we have space, time, and action?"
Actually, I think that it is possible, but the math is tensorial. Just like Joy's linearization of 3-D space, by reducing space to one dimension orthogonal to time, it would be a form of space that results in what we call matter objects. I will leave that as a homework assignment...