Ok, part 1:
"Bass management" infers that you set up the system so that no frequencies below a certain point are sent to the main speakers and that the subwoofer only plays below that point - so basically no overlap. It sounds to me that you have just that - overlap. Both the sub and the main speakers are playing at around 80Hz, doubling output there. You can't properly set subwoofer's volume until the crossover is first sorted out. You have to do just that in YPAO. Set it as recommended - subwoofer on, crossover set (80Hz is good) and main speakers set to low cut. On the subwoofer itself , set it at midpoint in volume with the crossover set at 100Hz or higher. Run YPAO. You dont' have to use the EQ in YPAO or the YPAO volume. Those are optional. Usind YPAO will automatically set the subwoofer volume. If it still sounds boomy (it won't) to you, you can cut the sub volume a notch or two.
If you are prefer not to use YPAO, you will need to set everything up manually and that's a big headache. Lots of factors come into play and you need a tone generator app at least to get it right. You can use SVS's (doesn't matter your brand) suggestions for the crossover with your speakers:
Use our Subwoofer Matching Tool to find the perfect sub for your home theater. Complete your audio system with a high end subwoofer from SVS.
www.svsound.com
Part 2:
Only if you need Amazon Music or any other new feature (there are few). The R-N803 is a very good receiver/amp. The display is much easier to read from a distance too. The amp sections of both units are remarkably similar. I wouldn't expect sonic miracles from the N800 - at all. IMO, only the jump to the N2000a makes sense, but it is expensive. A better alternative is a good, beefy amp like the A-S1200 and the Bluesound Node X - or the NAD M10 v2. All of the alternatives, as you can see, are much more expensive and
none of them are more than 10% better than what you already have.