I'm afraid I don't find the question terribly interesting, and I don't think it yields any information about the nature of computing.
That being said: Tom Stoppard had a character raise this idea in his play "Arcadia" (without recourse to a Turing machine-- the character was speaking in the early 19th century):
"If you could stop every atom in its position and direction, and if your mind could comprehend all the actions thus suspended, then if you were really, really good at algebra you could write the formula for all the future; and although nobody can be so clever to do it, the formula must exist just as if one could."
And, of course, that's trivially true, if the universe is made up of (properly atomic) "atoms" which possess no changing attributes other than a position and a direction. Unfortunately, current research in physics indicates that things are a fair bit more complicated than that.
So, let's generalize: if the universe is comprised of a finite number of (otherwise) unchanging atomic elementary particles, and if a finite number of types of transformations are permitted to each particle, given the total state of all particles at one moment in time, one could theoretically derive a formula to derive the state for the next moment-- if, and only if, you believe that the transformations and operations thus described are determinate.
In other words, if there is any true randomness (and not merely pseudo-randomness) involved, you're shit-out-of-luck. And, at present, we have absolutely no way of knowing whether or not that is the case, so the whole matter is purely idle speculation (which is why I find it not to be an interesting question).
Now, what does the above tell us about Turing machines, or the nature of computation? Precisely nothing that we didn't already know. The definition of what is computable remains unaffected.
Thus, the answer to your bullet point questions are:
- We have no way of knowing.
- Not much, with the current state of physics.
- A universe that is isomorphic to a Turing machine is determinate, and finite.
- It's pure speculation, and to the best of my knowledge, is not treated in the literature in any depth, for precisely that reason.