I would like to ask you one specific question - We need RNA polymerase to make a protein, but RNA polymerase is made up of proteins. So how does RNA polymerase, or its subunits, appear in the first place?
RNA polymerase is the main transcription enzyme. Transcription begins when RNA polymerase binds to a promoter sequence near the beginning of a gene (directly or through helper proteins). RNA polymerase uses one of the DNA strands (the template strand) as a template to make a new, complementary RNA molecule.