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Unfortunately it is still unclear to me what exactly is happening to the engine. So i will help the best way i can with the info i have,
First of all the overvoltage protection relay (OVP) must be replaced/resoldered. Very often it causes voltage supply interruptions to the idle speed control valve and many control units. The relay is located behin the battery, in the control unit compartament. You will recognize it by the fuse in it's top lid. It might be located under a plastic cover in front of the engine bay fusebox. I need the VIN to tell exactly.
Another pssibility to check, is the fuel pump relay. Due to cold solder problems inside of it, it interrupts the voltage supply to the fuel pump. It is located near the OVP relay, either in control unit compartment behind the battery, or in front of the fusebox.
It's fault is confirmed if you listen to the fuel pump when you are having problems- it will swithch off during engine running by itself.