fail-safe mode activated while.driving

What are you calling a "Fail Safe Mode"? The Battery light indicated a problem with the Charging System and the tool Icon indicates a Transmission concern. Sounds like you need to get it to a shop before you do some real damage

Took vehicle to get system error code. Status, fuel rail pressure sensor. Vehicle shuts off while driving..

Message code on vehicle: check fuel cap. Did. Let vehicle idle and still the same issues. Low oil pressure. ???

You're trying to fix it without diagnosing the problem. Codes don't tell the whole story: they only indicate that there may be a problem in a specific system. Obviously, a fuel cap won't make the engine stall and neither will a sensor - it doesn't "do" anything but measure fuel pressure. Lo oil pressure won't shut the engine down either. My guess would be that your fuel pump is failing but that's a $200+ guess. why don't you take it to a competent mechanic instead of guessing.