You ask a series of questions, sometimes expressed separately and other times embedded in your theses. I pick up some questions which I can isolate:
How does Newton's concept of absolute time change in SR? Answer: Absolute time is abolished, there is no absolute time in SR. The main reason is the contradictory concept of global simultaneoussness. In GR Einstein also votes against an entity which influences other entities, but does not experience itself any impact from other entities: Not only does spacetime prescribe via geodesics the trajectories of material objects. Spacetime itself is curved by the mass distribution.
How does Newton's concept of relative time change in SR? Answer: One can substitute the proper time along a trajectory for Newton's concept of relative time.
Is it correct that all inertial frames everywhere and at all times are the same? Answer: They are not the same, but Lorentz transformation transforms between the coordinates of different inertial frames. At most one can say: All inertial frames are equivalent concerning the description of nature. But note that GR extends the concept of frame transformation and allows also non-inertial frames.