We should probably avoid the words "global" and "local" since they are ambiguous. The transformation between the Minkowski chart and the Rindler chart covers more than an infinitesimal neighborhood (which is what "local" usually means); it covers a "wedge" of Minkowski spacetime to the right of the origin, bounded by the null lines ##t = x## and ##t = -x##. Whereas a transformation between Minkowski charts covers all of Minkowski spacetime (which is what you are using "global" to mean).there is no global transformation between a Minkowski chart and a Rindler chart for the simple reason that the Rindler chart is local(and doesn't include the origin).
However, a transformation that covers a particular open region of spacetime obviously covers any smaller open neighborhood within that region; so any such transformation is certainly "local".
Certainly not. Any Lorentz transformation--i.e., any transformation between Minkowski charts--covers any local neighborhood of Minkowski spacetime. However, that doesn't make the transformation between a Minkowski chart and a Rindler chart a Lorentz transformation.Are you then saying that there are no local Lorentz transformations?