5. It's a different show by late season 3. I've seen this point brought up a lot about the show. BSG goes from being a show about the survivors of Humanity making their way to Earth and fighting the Cylons to being dominated by angels, prophecies, and gods. You can really see the parallels to DS9 here, where the "Prophets" and Sisko as emissary arc became increasingly prominent whereas early DS9 was more politics-driven. Your mileage may vary on whether these elements made BSG a better show or not.
The debate of the merits of nuBSG has been done to death, and I don't want to enter into that again, so I won't comment on your other points. However, I did feel like this one point deserves clarification.
The original series of BSG took a similar turn with the arrival of the Ship of Lights and the Beings of Light, in "War of the Gods." The physical appearance of the nuBSG Final Five as beings of light is pretty clearly a shout-out to the BSG:TOS Beings of Light. Given what happened in BSG:TOS, the intervening of higher powers in nuBSG, who perform resurrection (in BSG:TOS it was Apollo who was resurrected), was completely logical and expected. This part of the story may have been influenced by DS9, since DS9 happened in the interim and Ron Moore worked on it, but it is plausible for it to have been exclusively something reimagined from the original BSG.