{x0,y0,z0} is a coordinate point with zero dimensions .
You are clearly assuming three dimensions and getting the notation wrong (use parentheses, not braces--braces are for set notation)
You are mistaken , a metric expansion is not an expansion of space itself .
Nope. it is actually an expansion of space itself.
ubble red-shift is based on visual matter , not of space .
Well, it is based on observations of galaxies, in part. But it is also based on observations of the cosmic background radiation.
There is no evidence and has never been any evidence of the space itself expanding as if some material .
And this is false. The evidence is the strong observational support for general relativity, where space is curved (along with time) by matter and energy. These are actual, measured effects.
The Big bang was written after Einstein ,
Using a solution of Einstein's equations.
Einstein meant space and quantum fields were indistinguishable , not interwoven as many now think .
Um, no. Einstein didn't do much with quantum fields. he was important in the early stages of quantum theory, but did not do anything with quantum field theory because he disagreed with some of the basic facts about the quantum world (including things we have actually verified since he died).
Space itself is independent of matter , there is no evidence to suggest otherwise as points of space do not move or can expand .
Wrong. Space expands, curves, and otherwise participates in dynamics.