Your heater core is clogged if your not getting heat in the cabin which could cause the overheating.
I would still test for exhaust gas in the cooling system.
Not necessarily. An air bubble in the system will also keep heated water out of the heater core. Shutting off water to the heater core will not cause overheating. The OP had recent work done on his cooling system which increases the likelihood that there is air in the cooling system.
