Some problem being too chaotic or computationally expensive to perform is a completely different thing that claiming something supernatural. And there is hardly any reason for computers to be confined to silicon digital logic, using coprocessors is a standard procedure, so whatever element if any which exhibits hypercomputation (which is highly doubtful as the universe barely even reaches even a small fraction of the possibilities of turing machines let alone beyond them) or otherwise more efficient classical computation, we can isolate the element and use it as a chip.
To be clear the limitation here isn't silicon logic, it's theoretical logic (specifically general recursive functions). It sure seems like any possible computation can be expressed as a general recursive function, but that's a scientific thesis, not a mathematical theorem. As we have yet to formalize "define a physical system" it is possible that this task isn't actually expressible in 21st century mathematical logic. I suppose some custom hardware which doesn't use logic at all might help, but then Gödel's theorem wouldn't apply at all. (Likewise with modal logic.)
Yes but as of yet physical systems have barely scratched even more than 0% of simple turing machines, so presently I'd consider that possibility a wild speculation.