Sounds like vapor-lock. At highway speeds it runs OK, perhaps because of better cooling and more fuel flow, preventing vapor-lock. Around town the engine compartment is hotter and less fuel flow, resulting in the fuel line getting hot somewhere, the fuel vaporizing in the line, cutting off fuel flow.
Solution: trace the fuel line through the engine compartment. Wrap insulation material around it from an auto store.
Also - because the overheating is worse in town, check that the radiator fan and its controller are working.
Working and blowing the right way. I’ve seen people reverse the wiring on those, which makes the fan suck hot air from the engine into the radiator.
Think He has a bad fuel pump relay. When the relay goes bad most cars have a oil pressure ativated bypass for the fuel pump relay. When the car stops in traffic the oil pressure drops too low to keep the pump running and the engine stalls. The car restarts when the oil cools enough resulting in higher pressure. On the highway the engine is running fast enough too keep the oil pressure up and the pump running