Engine overheating and temp inconsistency

I just purchased a used 96 Firebird with the Y87 performance option on the 3.8 L V-6. The car has 73000 miles and runs great with the exception of a weak O2 sensor, code 0133. The first week of driving, the temp indicator seemed a bit low at about 180 but stayed there for my 30 mile commute on the freeway and even in town. In the second week, all of a sudden it would climb to 210 and fluctuate a little. When it climbed to 225 in stop and go driving on a warmer day, I turned on the heater and it dropped to 200. I turned the heater off and it went back to about 210. Now the last 2 days, it will run at about 180 for a short period of time and then climb in steps with the highest temp being about 240 but when trying to cool it by turning on the heater, I have no heat, just cold air. The coolant level is fine but the cap when removed was caked with gooey rust. I plan on flushing the system and replacing the coolant but might the pump be clogged or in need of replacement because of the loss of flow to the heater core? Did GM put a shutoff on the heater lines during an overheat? Should I replace the thermostat or at least pull it for the flush? Thanks for any help...

Replaced pump, thermostat and flushed system. I was finally able to get the air out of the system to get heat out of my vents and maintain 195 degrees. Next day, this morning, the temperature rose again and no heat from the core. Before leaving work, I bled more air from system and again had heat from vents and a stable temp. Not losing much coolant if any except maybe a little from overflow as it cools. On the way home, overheat again and more air in system. Seems like a little fog on the inside of the windshield. Could a minor leak in the heater core cause it to suck air when cooling and thereby air-locking the cooling system? Any info will help...