Dear Jose,
I enjoyed reading your essay. A few thoughts come to mind.
1. Regarding the relationship between mathematical and physical theories, I agree with what you say. In particular, physics "deals with the fundamentals of this physical world," and hence basic physical principles should be the starting point of physical theories, not "convenient mathematics." Rather, the mathematics ought to be whatever it has to be to get the job done.
2. You make a good point when you say "One may fear that the present experimental pursuit may be abandoned for lack of funds - not due to lack of interest." I discuss a (very optimistic) possible way around this at the end of my essay here.
3. I quote from your page 3: "So what I suggest is the removal of the assumption that any mathematical idea can be used in physics. Then, the laws used in physics will have to be classified as physical and mathematical, the physical laws explaining the properties of the physical world, and the mathematical laws explaining how it works."
4. There are a couple of thoughts I might add to this. First, a lot of the mathematical assumptions that appear in modern physics are used because they are mathematically convenient, not because they have any obvious relation to physical reality. For instance, consider the concept of a 4-dimensional spacetime manifold. It involves concepts like "least upper bound property" and "nonmeasurable sets" which obviously have no physical meaning, yet it is retained because it is mathematically convenient. Or consider the mysterious "time dimension." I doubt if anyone will ever be able to prove that it is anything except a way of talking about cause and effect (cause precedes effect) but it is treated as a "dimension" because this is mathematically convenient.
5. Second, I will say that if you give up mathematical convenience, it can lead to some horribly complicated mathematics, much more complicated than what is used in conventional physics. I mention some aspects of this in my essay, without actually describing the math in detail. I think one essentially has a choice between mathematical convenience (in which case, the physical nature of what you are doing may be highly doubtful) or physical clarity and simplicity, in which case the mathematics may be very hard. I prefer to describe things in terms of cause and effect, and this replaces certain mathematical assumptions like manifolds and group symmetries with more obviously physical concepts like cause and effect and the ordering of events.
6. I agree that space and time are separate. I think that time is a way of talking about events that are causally related (since cause precedes effect), and space is a way of talking about events that are not causally related (because systems far apart from each other cannot immediately interact. I also agree that it is a useful idea to propose a finite "fundamental unit. " However, I think that such a fundamental unit may be much smaller than any particle we currently know about.
Thanks for the interesting read, and good luck in the contest! Take care,
Ben Dribus