how stable EEPROM is compared to PROM
Electrically-programmable fused PROMs suffer from bit rot and simply are not made anymore. I hate the damn things with a passion, they are one of the causes of good legacy test equipment turning getting bricked. The legacy OTP EPROMs require high voltage for programming and the only concern with them is slow charge decay. These days, it's FLASH all the way.
Alas, you're making up imaginary problems. Every high-rel firmware-based system will not only verify the integrity of the firmware upon boot-up, but continuously during operation. I mean, heck, we're not even talking about the cars here - my washer and dryer are both running continuous firmware CRCs in the background, all the time, as well as RAM integrity and plausibility checks.
Never mind that the inside of an ECU module is quite isolated from exterior noise. Every circuit going through the box has extensive filtering and surge protection. The logic supply voltages will be within spec all the while the battery voltage swings every which way (think of a range from single volts to a hundred or two).