Knowing that polymerase protein is needed for the transcription of genes, which polymerase is used in the transcription of polymerase protein itself?
In eukaryotes its RNA polymerase II. In bacteria it is the normal RNA polymerase. Although it is true that polymerases are now needed transcription of more polymerases, this mechanism may not have always been present. In the RNA world hypothesis, RNA coded for proteins and not DNA, so with the emergence of DNA, RNA polymerases may have formed as well. To produce proteins from RNA, organisms use complexes called ribosomes, which are ribozymes (RNA enzymes), which have undergone many rounds of evolution from original ribosomes, so there wasn't an issue with the production of proteins from RNA and throughout the course of evolution, polymerases were then developed, but they were only necessary with the rise of DNA.