Do all RNA polymerase in Eukaryotes share the same transcription factors?
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):



Source:

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.