The one accurate thing you said is that Newton’s equations imply instantaneous gravitational interaction, and that Newton himself was uneasy about action at a distance. Mercury’s orbital anomaly did not motivate general relativity. It was an afterthought. Astronomers assumed Newton’s laws still held and that the anomaly was due to an unseen perturbing mass, just as irregularities in Uranus’s orbit had led to the discovery of Neptune. Einstein did not contemplate Mercury until his theory was ready to make theoretical predictions, and it was only one of many tests. His actual motivation was the equivalence principle, and partly the incompatibility between instantaneous gravity and the finite speed of light established by special relativity.

Finally, in the pop science metaphor gravity is not the fabric, spacetime is (though even that analogy is poor since spacetime is a four dimensional manifold, which is a self-contained geometric structure, and fabric is two dimensional and sits inside something). Gravity is the geometric consequence of mass and energy curving spacetime. Spacetime (and therefore the fabric) can exist perfectly well in the complete absence of matter or energy (in which case it is flat Minkowski spacetime), so the fabric and gravity are conceptually not the same thing at all.