Engine keeps overheating?

The impeller can break off the water pump's shaft but that's more common on Volkswagens with plastic impellers. Are you seeing bubbles in the reservoir? If that's why you think it's overheating, that is due to a leaking head gasket. The clue is bubbles from boiling coolant will have steam associated with it. Bubbles from a leaking head gasket often don't produce much steam, especially when the engine is cold.

The multiple observations are conflicting but I have heard of similar situations caused by an inoperative electric radiator fan. Natural air flow at higher speeds cools the radiator without needing the fan. When standing still and not producing much power, many newer radiators are so efficient they dissipate enough heat to the surrounding air without needing the fan, but the added power needed for driving at slow speeds generates more heat. That's when the fan is needed. Check that first to see if it turns on.

The pressure cap only raises the boiling point of the water in the coolant. It's common for cooling systems to hit more than 220 degrees. A 15 pound cap increases the boiling point by 45 degrees.

Is there a belt-driven fan? If the condenser is off to the side of the radiator, the should be two fans. If the condenser is in front of the radiator, there will be only one fan. Check if that fan is turning on.

Ensure the clutch fan blades has not been installed reversely, which would affect the air being pulled by the fans and also the fan shroud is in good condition.

Based on the heater observation, it sounds like the coolant is stopping circulating intermittently. That could be due to a loose impeller on the water pump, but that's rare, a slipping water pump belt including those that are driven by the back side of the timing belt, and an air pocket by the thermostat.

Thermostats will not open in the presence of hot air. They must be hit with hot liquid. If a head gasket is leaking and allowing combustion gases to get into the cooling system, an air pocket could form by the thermostat and cause it to close. Hot coolant won't circulate to the radiator or to the heater core.

Your mechanic can test for a head gasket leak with a glass cylinder with two chambers partially filled with a special dark blue liquid. He draws air from the radiator while the car is running. If combustion gases are present, the liquid will turn bright yellow.