How can two proteins have identical amino acid composition, but very different functions?

Yes, all of those things you mentioned can alter the folding of a protein. Even supposedly silent mutations can alter protein folding. For example, in one of the proteins necessary for blood clotting a silent mutation was found that induces hemophilia. Even though there is a high degree of redundancy in the genetic code not even codon is equal.

i think the miocene epoch spans the time from 23 million to 12 million years ago.