I would expect you to be concerned, but you need not be concerned because of the conclusions, but, rather, because of the means to the conclusions. Generalizations, particularly if presented as axiomatic without even giving 'proof' of their veracity, are dangerous. You seem to want me to agree that they are axiomatic.
Are you suggesting that evidence is required of these things? I mean, with regards to Statement 1, I think it's obvious to everyone that in a given population of animals, that there are going to be variations among the individuals. You can spend an afternoon at your local shopping mall and see this for yourself.
Likewise, with regards to Statement 2 I think it's clear to most people that genes play a very significant role in what characteristics you have. My blonde hair, my blue eyes, my straight nose, the fact that I have the little dangly bits at the bottom of my earlobe, all these are examples of traits that are caused by genes.
Concerning Statement 3, I hope you already understand that parents pass on their genes to their offspring.
And with Statement 4, I hope that it's fairly clear that different traits can have an effect in how well the animal survives. If an animal has a gene that causes its bones to be slightly more brittle, then that can mean it will suffer a broken bone in a situation where another animal without the genes would not break a bone.
Likewise, with Statement 5, I think it is fairly clear that animals that have traits that help them (such as a slightly thicker coat in a cold climate) are more likely to survive for longer, and thus have more opportunities to reproduce. After all, the longer you live, the more time for breeding.
And as a consequence of the above statements, if an animal is able to reproduce slightly more than the average because it has genes which result in it having some advantage in reproduction (such as a gene which confers a benefit to living longer, or growing larger antlers and driving off rivals, that kind of thing), then the gene for that advantage can be passed to the offspring. And then the offspring will have that same gene. The chance that this gene will be passed on to offspring is going to be a bit higher than the average chance for some random gene to be passed on. Likewise, the gene that causes a disadvantage is going to be LESS likely to be passed on, since it would result in a poorer chance for reproduction, either by means of killing the animal (such as my above brittle bone example) or by making it less likely to breed (smaller antlers which can't drive off competitors).
If you require concrete examples of any of these, please let me know.