I know that TFII proteins bind to cis elements in DNA and help initiate transcription for RNA polymerase II. But do RNA polymerase I and III also use these proteins when transcribing genes? Also, do all genes require promoters/cis elements? Do all genes put in a vector require promoter regions/cis elements?
Except for the TATA-binding protein (TBP), there are no common transcription factors for each RNA polymerase. However, there are homologies between many of the factors used by the different enzymes.
The paper Conservation between the RNA Polymerase I, II, and III Transcription Initiation Machineriesa gives a good overview over the different initiation factors of each RNA polymerase enzyme. It contains a comparison of various transcription factors in yeast.
Here is an excerpt form the paper showing the homologies between some of the initiation factors of the TFII group and their homologous counterparts. (The first schematic is RNA poly II, the second RNA poly I, and the third RNA poly III):
a Alessandro Vannini, Patrick Cramer, Conservation between the RNA Polymerase I, II, and III Transcription Initiation Machineries, Molecular Cell, Volume 45, Issue 4, 24 February 2012, Pages 439-446, ISSN 1097-2765, https://doi.org/10.1016/j.molcel.2012.01.023.
Here you can find a variety of conserved sequences, not just in eukarayotes but across all organisms. RNA polymerase has only been extensively studied in e coli, where about 100 RNAP related genes have been found. All bacteria seem to share a set of genes such as rpob, terminal domains, and omega subunit. In eukarayotes you furthermore have the 5 polymerase proteins, which closely correspond to archea RNAP. Poxvriuses have their own similar RNAP.
As for retroviruses, the entire science behind them is rather vague so we cannot say exactly what RNAP genes they employ. It is claimed (without much evidence) that they employ a few genes labeled "pol" to achieve a similar functionality.
The promoter regions are not thought to be strictly necessary although they do greatly speed transcription if most genes. They are usually conserved as well.