The default for Regeneration is Fire and Acid.
I don't think I've ever seen Regeneration stated as bypassed by anything else, although it would be interesting to see regeneration bypassed by Cold.
(You know, 'cuz that would make sense)

Her use of "Necromancer" here is for lack of a better term. There's actually no "Real" undead involved (they count as constructs)
see thread title.

Fast Healing is Fast Healing. The Other necromancer gets it too, at the price of a feat or for free with capstone. The D8 HD PLUS fast healing may be a bit excessive, but I'm reasonably certain the fast healing is intended to counteract your use of the class abilities, such as overstrain. You're taking self-inflicted damage every round, and a lot of it. You'd need to playtest this at a variety of levels to determine if the fast healing is excessive.