With proofreading, the accuracy of DNA polymerases is about 1 mistake every billion base pairs added. All DNA replication is initiated by an RNA primer 2. Enzymes are catalysts for metabolic reactions. Enzymes bind specific molecules, called substrates, very tightly and position them very precisely so that covalent bonds can be rearranged at the body temperatures or living organisms. Etc., etc., etc.
Polypeptides have structural, regulatory, or enzymatic roles.
Not all genes code for polypeptides. Note that mRNA is NOT a final gene product. Amino acids are specified by specific, three letter combinations called codons in the mRNA sequence. Codons are translated by ribosomes, which polymerize amino acids into polypeptide chains. All mRNA is transcribed from DNA, and translated on ribosomes.