Car overheating

The radiator is a new one.

I attached a picture of my water pump and the way it is rotating. Isnt it going the wrong way? What can I do about this?

The following facts exist with the situation or have already been done:

1) a new water pump has been installed
2) both fans are working properly but still the water gets too hot in the system
3) There is no stuck thermostat because we pulled the thermostat out completely.
4)There are no major water leaks and the car is not losing any water really at all so that is not the problem.
5)The reservoir cap appears to be fine and sealing with all its rubber components in place.
6) whenever you unscrew the air bleed valve on top of the engine block, it temporarily fixes the overheating problem for a few hours or maybe one day, then the heating problem comes back.
7) The car and engine runs great both before and after the car starts to overheat. However, always pull over before heating gets into the red area on temperature gauge.

Knowing all the above things, I was thinking some of the below things might be the problem.

1) the radiator is not working properly, and therefore water is not circulating at all but just boiling in place. Maybe a good flushing of the radiator could fix the problem. How can you tell whether the radiator is blocked or not working thereby causing the water to just sit and boil?

2) I hear something about heater cores getting blocked but do not even know if a 2004 chrysler concorde has a heater core or if it did and it got blocked whether it could cause the car to overheat?

3)the head gasket leaks or the heads are cracked, but I do not understand how that could cause a car to overheat. Moreover, the engine runs super great - get up and go and everything - which causes me to believe that the overheating problem has nothing to do with a head gasket leak or cracked heads. Then again maybe a car can run just fine and haul but still have a head gasket leak or cracked head, as I do not know the answer to that?

4) Maybe the radiator works fine and the water is flowing thru the entire coolant system fine, but that somehow air is getting into the system, and it is only this accumulation of air that is getting in with the flowing water which is the overheating problem. However, if the overheating problem is solely caused by air somehow getting into the system with the water, then I do not understand how just air could cause the vehicle to overheat or how to fix such a problem?

Do you guys have any ideas on what is the problem with the car based on all the things I told you above?

Mike