I wouldn't count on the P3 or Freedom being waterproof. They should be ok in the rain but they're not dive lights. If someone tested one underwater and it didn't leak, they were lucky. I have a CMG O4 which also advertises itself as being waterproof, but you have to assemble it just the right way to get it to seal properly. Anyway, I'm not trying to knock these lights, just saying don't have unrealistic expectations. The Freedom comes with a cute little clip for handsfree use (clip it to your shirt collar if you're not wearing a cap), which looks nice. I haven't bought one yet though, so am going by other people's reports. I just haven't felt much point to spending so much on a coin cell light.
The P2 has even worse seals than the P3 or Freedom but it has no electronics to fail. If you get water inside it, just open it up and dry it out and it should be fine. Note you might have to replace the batteries though. I do have a bunch of P2's. For a long time my only EDC was a P2 with green led and 1x2032. I'd recommend that over the yellow. You get tremendous runtime, and it's closer to the wavelength where your night vision is the most sensitive. I'd say it's somewhat brighter than a white led on a 2032.
Yes you should be able to run the P3 or Freedom for 16 hours on medium with 2x2016, though it will be pretty dim at the end. Try it on low. It's amazing how little light you actually need to see well enough to walk around, once you're dark adapted.
Maybe the light you really want is a UKE 2AAA eLED. It's a lot bigger than a Photon but is waterproof to 1000 feet and has 20+ runtime hours at full brightness on two AAA's. The Peak Led 1AAA (very similar to Arc AAA but lower powered) is another possibility (
www.peakledsolutions.com ).
If you want a tiny light, there's some 95 cent 2xCR1616 ones from advancedmart.com. I just got a few of them since I sort of collect these things. They're not very impressive, squeeze-only and not waterproof at all, but they're only about 2/3 the size of a Photon II.