The building codes where I live are based on NEC codes. They're really hard to understand as a non-electrician.
Yes, PVC conduit will be fine, unless you're in a commercial or industrial application. Be sure to use grey PVC, although it costs a bit more. If you use white, some poor schlub (maybe me) will come along someday and cut through it thinking it's water (we always use white for water, yellow for gas, and grey for electricity).
You only need conduit below the bottom of the joists or running down a concrete or block wall. If the NM cable is run along the joist or through holes in the joist if run across joists, no conduit needed. It does need to be stapled or otherwise supported every 4 feet. Where you need conduit, flex is okay.
