Dang, I hit 'reload', but system was not showing me all you folks' posts until now. Thanks, everyone!
Answering your questions:
I got this inverter at the last minute after a friend blew up my good one. It was the biggest they had in stock at teh time. (I said, 'Don't plug that in there,' but he did anyway. THAT's what she said!)
The cables to the truck battery are about 12" long, unlabeled for gauge but pretty fat, and came with the inverter. The clip on connection is not great because the battery has side studs and plastic connectors. All that are accessible are the nuts on them.
Overnight, I ran the inverter off my house battery with fatter cables and an anderson connector. That was when it alarmed all the time over (probably) the laptop charger.
Ice won't keep frozen food frozen. I am not worried about it spoiling, just thawing. I'll have elec tomorrow night, next campground.
Am I really going to hurt my alternator?!?