Again, forgive me, but of course "natural selection drives itself" is a little....well, it doesn't make sense.
"Natural selection" is a label. It is given by evolutionary scientists to a process, a process that has two major factors. "Selective pressures" vs the "organism capacity to respond".
"Selective pressures" come primarily from the environment. Climatic change, resource change, predator-prey ratio, disease and so forth, put pressure on the organisms.
The organisms have a "capacity to respond" to these pressures. Their capacity to respond is informed by such things as physiological factors, genetic behaviours (controverisal, I admit), immune system responses and so on.
So we have "selective pressures" vs "capacity to respond". This process is known as "natural selection". It is "natural".
I don't understand what you are trying to say. Are you trying to say that God has some part in natural selection?!
of course, natural selection does not CAUSE genetic mutation. Genetic replication has mutations within it, sometimes. It might be beneficial, it might not. That's the "random" part of evolution. But those organisms with traits more suited to the "selective pressures" have a greater change of survival. In that case, the genetic mutation gets passed onto the offsrping, and is preserved.
The common ancestor is shown by genetic studies. We see that we diverged from chimpanzees. We then have a series of fossils that lead to homo sapiens. Granted, we have never found the "common ancestor". But so what? What's your point?