bad check valve or a leak.
Yes the Switch Hosting (Plastic) can leak due to Heat over the years.. Just replacing the switch can help it a lot..
Did you manually clear the codes ?
pressure switch
That indicates a fault and the switch needs replacing.
Low refrigerant defective pressure switch
It's probably overheating. If the pump is starting to fail, the motor will work harder to raise the same amount of water pressure. That will cause the internal thermal switch to trip, turning off the motor until it cools. If you're certain that the pressure switch is functioning properly, about the only thing left would be the pump motor.
A bad fuel pump can cause stalling. The oil pressure will show low oil on the lights or gauges but if the pressure is ok then the switch should not cause stalling.
It could cause a high reading on the gauge.
Only if installed incorrectly
I had the same problem. I took it to a mechanic and they told me it was the ignition switch.
No it will not.
Assuming you have replaced the fuel pump relay, try replacing the engine oil pressure switch/sending unit. It doubles as a safety switch for the fuel pump.