Lots of different questions there... The Parasound has basic bass management, though that's more than most. The Rotel, like nearly all integrated amps, offers full range preouts with no bass management. So we are clear, most subs have their own amp, so you wouldn't be powering it from the integrated in either case.
Speaker level can be fed to a sub equipped to handle that type of signal, but again, it is full range and you'd use the sub's x-over adjustment. Then the speakers would still be full range as well unless you used the sub's speaker level outputs, which would be at a fixed cutoff that is not adjusted by the sub's x-over.
In this case, the Parasound looks to offer the most flexibility, though the Oultaw RR2150 stereo receiver also offers basic bass management.