It is natural for your radiator to overflow with the cap off. As the fluid warms it expands, this is why the system is under pressure. For $40 to $50 get a Stator pressure tester and pressure test your radiator and cap. Of course the cap is cheap enough just to replace.
You fan operates at 2 speeds. Low speed and high speed. I replaced my fan motor after 155,000. It seized up. My symptoms were overheating in idle. The fan motor was intermittent. I happened to be watching on an occaision when it did not start. Like you I had a new water pump.
I believe my motor went as a result of years of operation with a bad thermostat.
The MAF would have nothing to do with engine temerature regulation. All it does is measure the volume of air entering the throttle air intake. This is used to compute air / fuel mixture ratios.
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Lets turn and burn.
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