Caveat: We are using Einstein’s second postulate about the constancy of c, but is it an empirical fact, ie., are photon worldlines the same for all observers? Yes: This is a direct result of the famous Michelson-Morley null experiment, though Einstein probably did not rely on their work in constructing SR. See Gerald Holton, "Einstein, Michelson, and the "Crucial" Experiment," in Thematic Origins of Scientific Theough: Kepler to Einstein (Cambridge, Massachusetts: Harvard University Press, 1973/1980). Yes, too, if we once again use the right math, namely the Lorentz transformation!