The RNA polymerases are numbered in the order that their products are used in protein synthesis.

RNA polymerase I makes ribosomal rRNA in eukaryotes.

RNA polymerase II makes messenger mRNA in eukaryotes.

RNA polymerase III makes transfer tRNA in eukaryotes.

The sigma factor is solely required for the initiation of transcription. In fact, the sigma subunit will often fall off of the enzyme during the elongation phase of transcription. Binding of the sigma factor is an important signal for transcription to begin.

The other subunits are crucial to the elongation and termination phases.

The codon AUG initiates translation in both eukaryotes and prokaryotes. Interaction with this codon by a tRNA molecule allows a methionine residue to enter the ribosome and serve as the starting point for amino acid elongation.

UGA, UAA, and UAG are mRNA stop codons and stop protein synthesis by causing the ribosomal subunits to dissociate and release the polypeptide.

Helicases are required for separating two DNA strands so that the rest of transcription can take place. Polymerases work on single strands of DNA, thus the bonds holding the double strands together must be removed. 

The correct answer is pioneer factors. Pioneer factors are able to bind DNA in condensed regions and promote euchromatin formation by recruitment of histone demethyltransferases and acteyltransfereses to modify proximal histones. Additionally, these pioneer factors recruit other transcription factors and co-factors to promote transcription. DNA polymerases are involved with DNA replication, not transcription. The RNA holoenzyme is a protein complex consisting of RNA polymerase, transcription factors, and regulator proteins that binds promoters and catalyzes transcription. 

RNA polymerase cannot initiate transcription by itself. It binds to the promoter but must wait for a sigma factor to bind to it. Now the RNA polymerase holoenzyme can proceed with transcription.

The correct answer is none of the other answers. Only mRNA transcribed by polymerase II undergo 5' capping, polyadenylation, and splicing. The C-terminal domain of this polymerase serves as a binding site and docking platform for many of the enzymes that initiate these processes. Moreover, experiments in which the CTD is truncated show that mRNA transcripts are not capped, polyadenylated, and spliced. 

The correct answer is RNA polymerase I. The sole purpose of RNA polymerase I in eukaryotes is to transcribe ribosomal RNA, with the exception of 5S rRNA, which is transcribed by RNA polymerase III. RNA polymerase III also transcribes tRNAs and other small RNAs. Transcripts of RNA polymerase II are 5' capped, polyadenylated, and spliced to ultimately be translated into functional protein. DNA polymerase IV/V are polymerases involved in DNA replication and repair.