Electrical Questions

So... turns out my girlfriend and I are going to be living in my van for the summer in her dads yard:h We're renting out the house. Needless to say I'm doing everything in my power to avoid using his house:R Beyond an extension cord anyway..... I built the van a few years back and it was designed to live pretty far off the grid for a trip i took up to AK and down into central America. Im about to be getting her ready for the summer and Ive got a few questions.

My lifecycle 6v 300ah batteries are charged by a small solar bank and a 40amp charger that comes off the alternator. This might be a dumb question but ive never dealt with using a converter. Is it possible to plug a 40 amp PD converter charger up to a standard 110v household outlet? I mean i know there are 50 amp and 30 amp hookups and cords but im pretty sure they are for 220v right? Either way im planning to just run an extension cord to the charger and then of course the charger to the batts but figured i should probably make sure its doable before i go ahead and get a charger.

Second question..... for now;) When i built the van i wanted to run the stereo off the aux batteries for obvious reasons, dont want to kill the starter batt. while i jam out to awesome music, but i dont think my electrical system has enough power to run the 4 6x9 speakers because the stereo shuts down when i turn it up too high. Is it possible to hook up a switch so i could choose to use the aux batts when im parked and the starting batt when the van is running? Or maybe the 4 6x9 speakers are just too much for the stereo to power and thats why its shutting down... in which case can deep cycle batteries this size power a stereo amp?

Thanks mucho for the help, enjoy the ride neighbors