No. Special relativity postulates that special relativity is preserved at all scales. It's an axiom. Comes from nowhere. It's assumed.

This is what a theory is: assume XYZ is true, and see how much of the world you can explain. Why is XYZ? That theory doesn't explain it.

Theoretical physics is: what is the smallest set of XYZ assumptions that can explain other theories. So if you can come up with a theory that's internally self-consistent that _predicts_ something which is postulated by another successful theory, that's a very convincing result.

It does, but a number of alternative theories of quantum gravity do not. So, if Lorentz invariance is shown to be violated, this would favor those over string theory.