Some of your questions have to do with DC, Some with AC. I will make the AC question red. The wiring practices for the two are different. In DC the ground and neutral are the same wire, (as in grounded to the chassis, and the appliance using the chassis for the return wire). In an AC circuit there is a black and white wire that carry the AC current, and a green wire that acts as a safety device. Some appliances do not use the third green wire and rely on being what is called being double insulated. But the outlet that you plug these into needs to have the green wire, (you may plug something into the outlet that does need the ground).
The batteries are actually 172 a/h per...they did figure for that. I'm not sure why the schematic says 100a/h.
Only about half of a batteries rating can be used. Drain them further and the life of the battery will be shortened.
should I run a ground wire from the battery negative output to the chassis?
Yes. Also if you use a 120 volt battery charger the case of it should be grounded to the chassis as well. The heavier the wire and thicker the chassis part you are bolting to the better.
Do I understand correctly that there is no a/c neutral...the neutral just goes back into the inverter? Is this what is called a "floating neutral"?
I think perhaps you are confusing neutral with ground? In an RV you do not tie the ground to the neutral wire at the breaker box like you would in a house. The RV is considered to be a sub panel. It relies entirely on the ground provided by what you plug the vehicle into, be it outside cord or inverter. The RV industry uses solid copper wire for 120 volt wiring, but I don't think this is a good idea. vibration plays hell with solid wire connections.
Do I just run a "live" wire from the d/c breakers to the lights and appliances, or do I need a negative to each light or appliance just like a/c?
If you ground the house battery to the chassis, it is possible to only run one wire to the appliance and then ground the other wire of the appliance to the chassis, But I would recommend running two wires. The grounds at the appliance have a tendency to get loose. There also may not be a good surface to ground to, (like a fiberglass top, thin sheet metal or a piece of metal that does not have a solid ground of it's own to the chassis. If something does make bad contact, finding the problem may be more difficult with only one wire, (where did you run the ground wire to and can you now get to it). Sometimes if the connection is just a little loose, the ohm meter will show the item has a good circuit, but when you try to pass heavy current through it, the connection is not good enough to allow the device to work.
[size=small] Can I run the van battery to the "first" battery in the system like in Bob Wells video about charging the battery with the van? Or where would it connect?[/size]
[size=small]Both the vehicle and house batteries should be connected to the chassis at their negative terminal, so to connect the two for charging only one wire needs to be run, (the metal in the chassis acts as the return wire). If you want to charge the house battery from the vehicle battery, [/size][size=small]t[/size][size=small]here should be a way to disconnect the batteries when the vehicle is not running. You can do this with a manual switch or a relay/solenoid. The wires between the batteries should be large enough to carry the charging current and there needs to be a fuse at each battery to match the wire size that you used. [/size]
