mmmmh i would be worried about this oil pressure thinggy IMHO...

check the thermostat, the fan fuse, and also the fan contactor, which could be faulty.

Maybe your oil pressure going down when hot is because you have very liquid oil, which is not viscous enough when the engine's too hot (because of the cooling not working) ?

to check the thermostat, remove it from inside its pipe, put it in a pan full of water, put it on the fire, and see if it opens when the water becomes hot.

I personnaly had this very precise problem last year, and this turned to be a thermostat not opening anymore. I saw it when i did the test i explained above