Overheating car that still blows out cold air when the AC is on

The AC system has nothing to do with the engine's cooling system. As long as the engine can still run, the AC will work. What you need to focus on is the overheating engine, if that is not fixed ASAP it will get worse quickly.

As long as engine temperature guage does NOT go past the halfway line , engine is normal.

Any time the temperature guage goes PAST halfway, engine is overheating and must be repaired ASAP (water leak or bad part) . Turn motor off . Recommended to toe vehicle at favorite garage to drop off.