1) One problem seems to be the ignition switch- it appears to stay in AUX, even after you remove the key. The heater resister only adds load to the heater motor "when it's on", to change the speed. If the switch is off, the heater should be off. Unless someone rewired something, I'd guess the ignition switch isn't turning everything off.
2) How did oil get to the tops of the pistons? Did this ever happen before? Try turning the crankcase nut clockwise with a large wrench, and see if the engine moves. Pull the battery, charge it up, reinstall it and try to start it again right away.