Can't really answer the first question (I assume PBS knows better than me) although of course there could be a lot of DNA with functionality we don't know about.
On the second question though, we aren't building proteins using any kind of DNA model, because what DNA specifies is the order of the Amino Acids (residues), which is what we start out with as given. The idea is that someone could take some DNA and translate that into a string of amino acids, and then use something like DF to figure out what the structure of the protein will be (ie how its shaped, how it's folded) given this ordering of amino acids. In other words we aren't "building" them in the sense that we already know what the DNA has told us - that is, which residues (AA's) are in which order. All we do is fold them.
As to the last question..... well I don't know, but genetically engineering ourselves is a big "what-if" question, as well as "can we" and "if so, should we". All these questions have been asked by a lot of people in journals, books, even movies (ever see GATTACA?) etc. That's probably the subject for another thread, or perhaps even another board