An inverter for the PSU? It's a DC-DC power supply, there is no inverter and it's higher efficiency than a AC-DC power supply.
Yep, dual core Atom would suffice. If you look at the parts I purchased versus the cost of similar Atom based parts you will see that they are very close for comparable motherboard features (I think the Atom was actually a hair more because I got a combo deal). As for power draw, right now you can see in the photo that it's running off of a AC-DC power supply. I have it plugged into my Kill-A-Watt just out of curiosity and the draw is ~60W average (and it's not an 80+ PSU).
In the car I'll also be powering a 7" touchscreen [12V], a USB (laptop) CD-ROM drive [5V], and a USB hub [5V]. I have an old M1-ATX which is rated for 90W, but to play it safe I got a new DS-ATX which is 220W max. I figure the most I'll ever possibly draw is 110W.
As for the amplifier, it is kind of a beast. I never do run it anywhere near it's maximum though.
I'm not in the least bit concerned though as I ran the same amp + a Carnetix P2140 in my previous vehicle: the 2003 Saturn ION. The Accord I have is a V6 and its alternator definitely puts out more power than that in the ION. I've already checked. Just to play it even safer I am upgrading the big three