If you are getting 0.5 V at the female receptacle of fuse #13 then that is not good. There is a 6 gauge wire that carries electrical current from the positive battery post to the PDC. From images you have posted this 6 gauge wire at the battery post clamp is suspect.
The original battery clamp has been replaced with an after market type clamp. This type of clamp leaves exposed wires and invites corrosion over time. Remove the clamp and clean all the indiividual wire strands and either clean mating surfaces or install a replacement clamp. Once this has been done repeat voltage measurements at fuse #13. Voltage should be around 12 volts.
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You are using a jumper wire on the LOAD side contacts of the starter relay. This circuit is independent of the circuit in question powered by fuse #13. That is why the starter spins the engine with a jump wire.
The control side of the starter relay needs 2 items present to activate the relay coil and cause the LOAD side contacts to close. Proper voltage power through the ignition key switch when turned to the START position. Simultaneously the PCM must provide ground to the starter relay coil. Constant (not switched) battery power probably must be present at the PCM for it to cause the ground to become activated for the starter relay. Constant PCM battery power or low voltage power through fuse #13 is missing so the PCM will not ground the starter relay. No starter activation is the result.
Again this is same result because of no constant battery power to the PCM. PCM will momentarily ground the fuel pump relay for 1 - 2 seconds when ignition key switch turned to ON / RUN position. Since no constant battery power or low volage power to the PCM as in the starter relay description above, PCM will not activate fuel pump relay.