well the power steering will shut off when the engine does because the belts stop turning the pump.

your car isn't lowered so i wouldn't expect the turned wheels to be chewing into the harnesses under the fenders, but i would definitely look to see if there is any wiring exposed or rubbing, it could just happen to touch another wire or metal and short out from the momentum of turning left.

it's probably not the battery or alternator, but does sound electrical. probably give the harnesses a good once over and stuff.

and yeah it's a nissan that's older, so it's gonna have some problems, but its still a clean car and you can fix it or be like me and fix, sell and bail out to a new car hehe.