Neo-Darwinism and the Survival of Genes in Gene Pools

I'm not a scientist, I'm a software developer and I don't pretend to understand genetics deeply but it's important to me that I understand the principles of natural selection - not just the process that Darwin outlined but the modern 'Neo-Darwinism' understanding. So, i'm going to quickly outline how natural selection actually works as I understand it.

Neo-Darwinism is the modern understanding of the process of natural selection (the 'engine' behind evolution). It is a gene-centric view of life and something that Darwin had no idea about as the science of genetics had not been developed during his lifetime.  'So, what is the modern understanding of natural selection..?:

1. Natural selection is the non-random (see point 2 below) survival of randomly occurring genes in gene pools (genes 'live' in gene pools)
   
2. Genes make bodies (like our bodies) - the genes that make bodies that are 'good' at surviving in their environments are the genes that will be 'naturally selected' and therefore will survive. Genes that make bodies that are not good at surviving will be 'naturally de-selected' - i.e. they will not survive.

Technically, it is genes that survive and get passed down the generations (if they are good at producing bodies that can survive well in their environments). Bodies do not survive, individuals of a species do not survive - the physical body dies but if the individual is successful at passing their genes on then the genes will survive. Our bodies are basically survival machines for genes. Sorry about that if you thought your body was a temple.

This is a fact - even if not a single fossil had ever been found, there is hugely enough evidence in genetics laboratories around the world to prove time and time again. It is not disputed, the physical evidence is there and even if it were the 'only' evidence it would be enough to prove the fact of evolution by natural selection. If you want to argue that natural selection is a 'theory' then you should lookup what is meant by the word 'theory' in the scientific world. To make it easy here is the link to the Wikipedia definition of the word (see the scientific definition):

http://en.wikipedia.org/wiki/Theory

The 'theory' - if tested (which it has been over and over again) always works and is the only explanation that works and can be tested.