The sigma factor is an important part of initiation for prokaryotic transcription. Once transcription has been initiated, however, the sigma factor is released during elongation. RNA polymerase synthesizes the RNA product until it is interrupted in one of two ways. In rho-dependent termination, a rho factor protein interferes with RNA polymerase binding and causes it to release the DNA strand. In rho-independent termination, structural features of the DNA cause RNA polymerase to become detached. The structures include hairpin loops, which generate steric hindrance, and adenine-rich sequences, which lead to weak binding of the RNA product to the DNA template.

Inactive RNA polymerase must bind to a specific sigma factor in order to become active in gene transcription. Sigma factors are specialized transcription factors involved in recruiting and activating RNA polymerase. Only once RNA polymerase has bound the sigma factor can it identify promoter sequences and initiate transcription.

mRNA is the product of transcription and is not involved in prokaryotic RNA polymerase recruitment. An RNA primer is essential to recruiting DNA polymerase for DNA replication.

RNA polymerase does not interact with the Shine-Delgarno sequence. The Shine-Delgarno sequence is present on some prokaryotic mRNAs and serves as a ribosomal binding site for the initiation of translation. RNA polymerase is only involved in transcription and will bind to DNA, not RNA.

The other answers are all true and unique to prokaryotic transcription. Eukaryotic transcription is much more tightly regulated by transcription factors and DNA packaging (chromatin), and is confined to the nucleus.  

Prokaryotic transcription occurs in the cytosol, since prokaryotes lack a nucleus. This allows ribosomes to interact with RNA even while it is still be synthesized.

In contrast, eukaryotic transcription occurs in the nucleus. Once RNA has been synthesized it must be transported from the nucleus to the cytoplasm before it can interact with ribosomes. The newly-synthesized RNA undergoes splicing to remove introns, addition of a 5'-cap, and addition of a poly-A tail before it can exit the nucleus. These modifications help prevent degradation of the RNA. Only after these modifications can the RNA leave the nucleus and becomes functionally active.

Shine-Delgarno sequences are ribosomal binding sites slightly upstream of start codons on prokaryotic mRNA. Eukaryotic mRNA is more complicated (it does not contain Shine-Delgarno sequences) and contains promoter regions that are responsible for recruiting translation factors and ribosomal subunits. 

While prokaryotic and eukaryotic transcription processes are quite similar, there are some key differences. One significant difference is that prokaryotic transcripts can contain multiple genes, which will then transition as a single RNA strand to the ribosome. This is referred to as a polycistronic transcript. Eukaryotes have only one gene per transcript.

Both prokaryotes and eukaryotes use promoters. Prokaryotes do not have nuclei, though transcription and translation can occur simultaneously and in close proximity in these cells.

In bacterial cells, binding of a sigma factor to RNA polymerase is required for the initiation of transcription. Once the sigma factor binds, RNA polymerase is referred to as a holoenzyme and begins to make the RNA transcript.

The operator region is the location where the repressor binds. Other parts of an operon include the promoter (where RNA polymerase binds), and structural genes.

Addition of 5’ cap, 3’ tail, and intron splicing occur in eukaryotes, not prokaryotes. Repressors bind to the operator region of the gene and prevent RNA polymerase from transcribing the gene, while activators bind to the promoter and increase transcription of the gene.

A repressor is a molecule that binds to the operator region of a gene and prevents RNA polymerase from transcribing the genes. An inducer can bind to a repressor, preventing the repressor from binding to the operator region, and thus allowing RNA polymerase to transcribe the genes.