Dear Akinbo Ojo,
I introduced the character of Prof Priss for two reasons: (i) to provide a third example of the effectiveness and reliability of mathematical laws in describing the physical world (after the examples from acoustics and knot theory), and (ii) as an opportunity to briefly discuss Tegmark's conjectures on the mathematical universe and to speculate on their possible future developments, as embodied in the Priss-Goedel-Priss theorem.
I understand that Tegmark's conjecture does not address the continuous vs. discrete issue (which, by the way, was the subject of the 2011 Essay Contest), and is open to both. His mathematical structures may be continuous or discrete, or, I believe, even include both continuous and discrete pieces; and all these structures are 'real'. Because the discrete/continuous discussion is not central in the Mathematical Universe, Priss does not take a position about this issue. Rather, he focuses on an aspect - the Self-Aware Subsystems - that I find intriguing in Tegmark's work, and makes it the subject of his theorem.
In conclusion, I don't know how Priss would answer your three interesting questions. My personal take on them is, in brief:
1. I regard infinity and infinite divisibility as logical constructions of the mind, not corresponding to physical reality, which is finite in all respects. 'Atoms of spacetime' are sufficient for building a very rich universe.
2. If these atoms are all there is, you do not need separating walls: they are separate by definition, like the integer numbers: what is there between 2 and 3?
3. Does the bottom mathematical structure, or algorithm, exist eternally? Under the computational universe conjecture, space and time emerge as the computation unfolds, so in a way there is no time before the computation starts, and the question would be meaningless. Whether mathematical structures exist 'before' the birth of the universe, or 'out' of time... I confess that I find these questions too difficult, or unattractive, or both.
Ciao
Tommaso