Remember one of the Cylon Loyalty cards can draw 5 damage Galactica tokens and keep two

a) Can Pegasus be damaged this way? If so then if Pegasus is damaged twice it is dead, because the CYlon wil draw two damage Galactica tokens from a choice of 5

b) What happens if the Cylon reveals this when on New Caprica? Theoretically it could destroy Galactica. And by the way, does damage stay on Galactica when Galactica leaves and comes back during New Caprica?

Not really, Pegasus can be damaged 4 times before dying. In the rules it does state any damage being delt to Galatica can be assigned to Pegasus instead though, so you are correct that a Cylon with that flip can choose two of the 4 damage tokens on Pegasus instead, unless its in errata later.

As for the New Caprica question, I can tell you that the Galatica DOES remain damaged while not in orbit, however you leave her when you go to New Caprica is how she returns. However, I do not know how the Cylons ability to Damage her works when shes not in Orbit.

I would assume it still does, or it would be in the rules as an exception, and it is not. So I guess if you leave Galatica with 4 damage and the cylon decides to not to flip the moment she hits 4 damage but instead goes down to Caprica and does it there, she would explode where ever Adama took her and the game ends.

Page 16 of the Pegasus rules: you can't damage or repair Galactica (or Pegasus) until she's back in orbit.