This belief is... unusual, to say the least. Your cells can most certainly mutate, that's what cancer is.
But it isn't just your own cells that mutate that drives evolution. The DNA you inherit from your parents is not identical to theirs. There are,
on average, 70 mutations in your DNA that your parents do not have.
There have been incredible amounts of research done into the evolution of different sexes. Start
here. Don't stop there and don't dismiss it just because it is a Wikipedia article. Use the links at the bottom to truly learn and understand how sexual (as opposed to asexual) reproduction developed.
I don't know why you think that. Bodies decompose. The gas you put in your car comes from oil that formed from the decomposition of the dinosaurs.
Not to mention that humans as we know it have only been around for approximately 200,000 years. Also, we have bodies that date to almost
300,000 years ago.
Written symbols, language, and record keeping are a recent (relatively speaking) development. The oldest written records we have go back to the
Jiahu symbols found in China that date to 66oo BC, well before the 4400 BC creation of the earth derived from a literal interpretation of the Bible.
And every single one of them is subject to mutation and natural selection.