The different pairs of nucleotides have their own properties that allow different functions. For example the pair AT uses 2 hydrogen bonds to bridge the two nucleotides together. Whereas the CG pair uses three hydrogen bonds. Thus, in areas of higher CG presence the DNA is more tightly coiled. Also, the tightness of the DNA coil can affect the ability of certain binding partners to fulfill their role because of steric strain.
I wonder what the presence of the oxygen on the sugar portion of DNA does to the structure and function. Perhaps it affects the way that thymine binds to the backbone. In this was it could maybe form more stable bonds with uracil. In addition, it’s possible that the presence of the oxygen on the RNA sugar could contribute to some of the other functions of RNA, like its ability to interact with different cellular machinery.
The mechanisms of the enzyme that moves this process along is probably similar to the way that amino acid chains are polymerized. Although in that case it is a peptide bond and in this example it is a phosphodiester bond, I imagine the processes are still similar. I believe that the enzyme that functions to establish the phosphodiester bonds in DNA is DNA ligase, which does exactly as its name implies.