Yes, P2 means Photon II (my abbreviation). LRI likes to say Photon I, Photon II, and Photon 3 (roman numerals for 1 and 2, arabic numeral for 3). I don't know why.

If your Photon is still bright, I don't see much need to change the battery, especially if you haven't been using it a lot.

I've never been that crazy about the P3. The Freedom really is an improvement, if you want a dimmable light. The P2 is still my favorite because of its simplicity, but I'm sort of a throwback.