Engine badly overheating

Just a general engine overheating problem here.
Lately it has been having some serious issues. These are the symptoms:

It will overheat to a serious degree so much so that the temperature gauge will be pegged, and it will have trouble starting when after shutting off. The check engine light comes on of course, but this is also sometimes accompanied by the oil pressure light, and yes the oil pressure gauge will drop to nothing, and then pick back up to normal when I accelerate but drop back to zero when I take my foot off the gas pedal. {I know the oil pressure light will come on sometimes if the engine is too hot in general, but what about the pressure gauge acting strange?} So I had the oil changed hoping that it was a viscosity issue and new oil would solve the pressure problem, but no, its still happening.

Before this it was also having some disturbing cooling problems, it would blow cold air while the heater was on and the temp gauge hot, I thought maybe it had some air bubbles in the coolant because it was contracting the upper radiator hose and steam was coming from the coolant reserve tank -which would empty completely. So I topped off the coolant, put on a new radiator cap and tried 'burping' the radiator, but this also did not seem to work as the engine is still overheating.

So right now im suspecting four things:

(1) maybe the water pump is on the fritz, so that the engine is overheating to a degree that it would cause the oil pressure probs. -Maybe the oil becomes too thin when very hot and will not circulate properly? The failing water pump would also explain why the vents are blowing cold air, because the hot coolant is not being moved over the heater core.

(2)The oil pump is failing, which of course would cause the engine to overheat. But then why the cool air blowing when engine is hot?

(3) The belts do not have proper tension which might for all I know cause all of these problems.

(4) The electric radiator fan is malfunctioning, causing the engine to overheat. A long shot but maybe the easiest fix.

Please let me know what you think, maybe I am way off on all four, let me know if you having any questions that might help you answer this riddle. Thanx in advance.
-Joshua