Car is blowing cold air when the heater is on , frequently overheats and smokes from the top of the radiator. I add water to the radiator and that will sometimes help or it start dibbling out underneath radiator,

 

welcome to the forum. aircondition mixer may be the problem for the cold air with heater on. frequent overheat may be your radiator top area is becoming clogged from corrosion. leaking under pressure. if you can do a pressure test on the radiator you may find a leak. if you have not changed your radiator anti freeze since getting the car it may be clogging. (this is without knowing the history of your car)

 

Replaced radiator and that seemed to help the overheating but still not heat

 

Sounds like the heater core is clogged
You can try cleaning by reverse flushing the heater core
Or you can replace it ( that would be the last thing I would want to do)
Sometimes a product that can flush the radiator will help flush the heater core also??

 

Let the engine run with the cooling system full.
If bubbles continue to come up into the neck of the radiator with the radiator cap off, you have problems.
Those bubbles are compression from the engine.
You then need a head gasket.
Any reputable shop can test that air in the radiator for compression residue. That will prove a bad head gasket.