About the finite divisibility of physical objects: rather than the need of a distance interval to insert in a division, mentioning atoms as roughly indivisible parts of material objects, would be more directly clear, wouldn't it ?
"there is a limit to the number of extended points or fundamental lengths, but there is also no distance between those points, since that distance will also consist of points."
There is a limit to the number of atoms, but there is a distance between atoms. That distance does not consist of atoms ; it is subject to a quantum uncertainty, that is smaller than this inter-atom distance (in the case of a covalent bound), but still quite bigger than the Planck length, which is thus irrelevant here.
"where to cut is a problem" : I don't think butchers see it so.
"Then, as you turn the screw further, beyond the sub-atomic scale of quarks towards the fundamental scale of length, ~ 10-35 m, the unexpected happens. At the scale of the fundamental building block, the blue extension is ultimately made of a featureless length, same with the yellow, green and red strips. At that fundamental color-blind scale, how is the boundary to be demarcated, say between one blue strip and another blue strip or between a blue and a yellow strip?(...) reality is fundamentally One thing"
You are telling a lot about what happens at the Planck scale. How can you know that much on what it actually looks like at that scale ? Colored objects are made of atoms; the information of color is carried by these atoms. Thus the division defined by colors cannot go smaller than the inter-atom distance. There is no point to develop qualifications about what happens when trying to physically cut at smaller scales, since we have no way to even try physically cutting things there. All we can do is take our best mathematical theories of physics, which were verified by experiments, and discuss what they mathematically define at smaller scales (quantum fields, structure of nucleus...). But we still don't have verified mathematical theories of what happens at the Planck scale, so I see no sense of even developing a discussion about it, as you did, as if we did have things to say there. Personally, I think it is more interesting to discuss the things we know (quantum physics), which already have interesting consequences on the issue (position uncertainties of atoms at the atomic scales), than writing an essay about how things look like at the Planck scale (which we actually don't know) in ways that ignore the known quantum uncertainties at the atomic scale.
"possibly at a future time, [space] would collapse, reduce to the minimum length and disappear (Big crunch)" : this was considered among scientific hypotheses before the discovery of the acceleration of expansion by dark energy, but since this discovery, the Big crunch is not considered scientifically plausible anymore.
"Quantum mechanics, an object, e.g. an electron at a location in the atomic orbit can without seeming to traverse the 'space in between', arrive at a different location, the so called 'quantum jumping'"
The electron does not jump from any definite position to any other definite position, because it never has any definite position. "Orbits" are not states of definite position, but states of rather definite energy. To be more precise : quantum states of the atoms are in a Hilbert space where can be defined a Hamiltonian operator that distinguishes "distinct energy levels" by its eigenvectors. Depending on circumstances, we can consider a given atom to be in a specific energy level in the list of possible energy levels (eigenvectors of the Hamiltonian), but nothing generally obliges this. The energies of these levels are defined down to a quite thinner accuracy than the intervals between these energy levels themselves. However they are still not infinitely precise, since atoms are not isolated systems but interact with their environment, at least the electromagnetic field. In particular, the typical time it takes to emit a photon, defines a quantum uncertainty on the interval between energy levels themselves.
So, since orbitals are not states of definite position, any question of "space in between" is senseless.
"extended points may not be eternally existing physical objects"
Before wondering if they are eternally existing, a first question would be whether they are physical objects at all. Basically, "extended points" is just an English phrase. It is not clear if this phrase can make any sense in physics, and which one, depending on a theory of physics that we need to specify as a reference if we want to give our English phrases any precise meaning.
"but can appear and disappear spontaneously, or when induced to do so"
Do you allow for a quantum uncertainty on whether or not they did ?
"I crave the reader's indulgence here to temporarily set aside current doctrine on the eternal existence of points"
I never heard about any such doctrine, as concerns physics. (There is no such doctrine in maths either, since "eternal" should refer to a stability along time, but Euclidean geometry does not admit any concept of time in the first place, so that there is no quality of eternity either to be formulated and claimed in the mathematical language of geometry).
I might continue another time with the last pages, but to tell my general opinion: I see this essay as rather boring, with ideas more repeated than developed, and not well related enough to what is actually known about physics. On roughly the same topic, I found the essay by William T. Parsons, "Are Boltzmann Brains running Hilbert's Hotel?" much more interesting and relevant. See my comment there about the issue of the infinitely small.
