1. Manufacturers have connected generators to either chassis, or house batteries, over the years. Which is best is anyone's guess. Mine happens to be connected to house-batteries, but my converter/charger also charges the chassis battery and house when running or shore-power or generator.
If the house-batteries were too low to start generator, the problem could be overcome by starting the MH engine which allows the alternator to charge both sets of batteries. Since the alternator supplies 70 to 100 amps at 14.5 volts running the engine will make starting the generator much easier.
2. Because many people are now using inverters to power more items while on battery-power only, it is much easier to lower the battery's capacity from under charging and causing sulfation. This, or having a voltage drop from too many items "on", will lead to insufficient voltage (and amps) to get the generator started. Since the generator needs current to keep running the battery-bank it may have a "net loss" and not be charging which will lead to generator shutting down. This problem more likely to occur from too small a single or multi-stage charger for the amount of power required.
Mark & Jan "Old age & treachery win over youth & enthusiasm"
2003 Fleetwood Jamboree 29