Akinbo,
That your digital wristwatch outputs a discrete value doesn't mean that it operates by the quantum principle of superposition. The values on the dial of your analog clock completely correspond to the digital output, as a continuous record of elapsed time.
"ALL the experiments and postulates of Special relativity were not carried out in a straight line! According to GR, no line on earth is straight! Maybe only slightly curved but definitely not straight."
Mathematically, a straight line is a special case for a curve. Light always travels (by Fermat's principle of least action) in the straightest line that it can. A light ray parallel to the Earth's plane travels straight out into space; Earth's gravity is far too weak to affect its path. In the case of Einstein lensing, however, a light ray traveling around a very strong gravity field, such as the sun, will curve ever so slightly so that the information the ray reveals about its source appears slightly displaced in space from the real source of radiation. The corrections you're worried about don't matter, except at relativistic distances and speeds. Otherwise, Newtonian physics works just fine; time and space can be treated as if they were absolutely flat and straight.
"And there was no quantum proposition as at the time SR and GR were formulated."
There certainly was. And it was due to Einstein himself, through his work in such things as Brownian motion, and the photelectric effect. See Einstein, 1905, "On the Electrodynamics of Moving Bodies."
Best,
Tom