FUEL PROBLEMS WITH 2000 CHEVY IMPALA...?

From your lengthy description is sound like you may have a catalytic converter going bad. When they start to go bad they inner guts of it will heat up as you drive the car until they expand out and clog your exhaust system making it impossible for your engine to exhale the burnt exhaust from the engine. When this happens it creates back pressure on the engine until it starts cutting out and finally shutting down. After it sets for a couple of hours and the converter has time to cool off it releases the back pressure allowing the engine to start again for a little while until it warms back up and the whole process starts again. To have this checked you will need to take the car to an exhaust shop and have then run a back pressure test on the exhaust system. Also keep in mind that you may have two or more converters on the car.