PSU Selction

First, I'm not sure I like any of those PSU choices, but if limited to the ones you've listed, the last one (NRP-PC402) is probably the one I would choose. If available, I'd strongly suggest getting a 380W Antec Earthwatts, 400W Antec HCG, or 400W Corsair Builder instead. Seasonic has some ~$40 80+ bronze 300W-350W units that would also be good choices, although they don't have a PCIE power connector, so you'd need to use an adapter if you ever upgrade your GPU.
Second, maybe. Many will, but some see the incoming waveform as unacceptable and will shut down. My Antec SG-650 is like that, and my wife's Earthwatts may be too. Cyberpower has a couple of units (with "APFC" in their model numbers) that aren't exactly true sine wave, but will work with an Active PFC PSU.