Hi,
Is it modified sine wave or pure sine wave? Battery chargers are inductive devices and may not produce full power on MSW.
The smallest "converter" is about 40 amps output DC with an input of approximately 700 watts AC (if the house batteries are "hungry"), so a stand alone 20 amp charger may be the biggest you can run.
A 400 watt inverter represents about a 40 amp load to the electrical system, so it would be best to have the engine running when ever the inverter is to be run for more than brief periods of time. Be sure to lift the hood on the truck to help keep the alternator cool.
If the battery bank is "hungry" you may get a lot more amps going in by using jumper cables.
