Where do future life extensions take place? Is this done in another dimension or is there a parallel physical world somewhere our soul extensions can inhabit?

As you have expected, this is a parallel world, but in another dimension, so it is an Earth-like plane that varies enough vibrationally that it is invisible to the universe you inhabit but has similar characteristics and allows a similar array of experiences to play out. So it is, in effect, a twin in all respects, people can come and go from the parallel world as well as the earth plane proper as you are experiencing it now in the physical. This, in fact, is a set of worlds because the future extensions are variants that are in their own dimensions, and this keeps things orderly so there is some separation that allows crosstalk of energies but not an overlay and interference directly, in a functional sense—only when there is a communication of sorts and a transmission of karmic force from one dimension to another.