2002 Hyundai Santa Fe Trouble

The "Battery" warning light has been telling you the charging system is no longer recharging the battery while you're driving. The other lights are in response to the resulting low electrical system voltage and those computers becoming confused or turning off. It's not common for an engine to run even an hour after the "battery" light turns on. The last thing you want to do is to ignore that light and keep driving. The engine IS going to stall, and you could be stranded a long way from help. The most likely cause is a defective generator, but your mechanic will test the entire charging system to know for sure.