I'm trying to figure out how this circuit work.
if both wires from C of the oil pressure switch and A3 of the relay are live and spliced- doesn't it make a short or sparks?
In normal operation, both wires have essentially the same voltage on them--therefore it's not a "short" circuit, and there'd be no sparks unless the insulation on the wire is broken and the wire grounds on something.
When one wire has voltage but the other doesn't, there's most-likely a switch open--either the oil pressure switch contacts, or the contacts within the fuel pump relay. So again, no "short" circuit, no sparks. If one wire doesn't have voltage because it's broken...sure, it could short to ground at the break and cause a spark, which would likely pop the ECM-B fuse.
and if there's no oil pressure, the pump is still getting power from the relay, so what makes the engine to stall?
There's nothing in the fuel pump wiring and parts that can turn the pump off with no oil pressure, IF the fuel pump relay system is working properly.
If the engine stalls with no oil pressure, the fuel pump relay system is probably faulty.
DOES THE FUEL PUMP PRIME when the key is turned from "Off" to "Run"? Could be the ECM, could be the relay, could be the wire harness connecting them, including crappy contact with the relay where the relay plugs into the socket.
But maybe the engine isn't stalling from lack of fuel. Maybe it's stalling due to some other fault. Engine stalls, oil pressure goes to zero--instead of oil pressure goes to zero and then the engine stalls.