Why is the carpet / floorboard wet at the accelerator pedal?

I think Heater core is good, passenger side is bone dry. Would heater core cause rust on driveway? Not antifreeze on floor . only water.

Your firewall drains could be clogged, allowing water to build up in the cowling area under the windshield wipers. More likely cause is that the little rubber bushings under the wiper arm (they fit around the shaft of the wiper transmission - the wiper arms sit on top of them) have rotted out and are allowing water to penetrate behind the cowling. I just replaced both of mine - they are cheap parts, but a bit hard to find. All they are, is small, flexible rubber caps that fit down over the stem - they don't attach to the car itself. But I had a similar problem and that was allowing water into the passenger compartment. Having rust stains on the floor, leads me to think your issue is probably the former - as water slowly leaks through the plugged drains, you are probably getting some battery tray rust. That would be the first thing I would check, after ensuring the wiper boots are in place.