P0191 has to do with sensing incorrect fuel rail pressure, either too low or too high as opposed to what the PCM is expecting.
P0562 has to do with the system seeing low voltage when is below 10 volts for a long enough period of time.
P2534 has to do with problems in the ignition circuit and maybe not enough voltage for that circuit.
P2635 has to do with electrical circuit to the fuel pump.
I am shortening all explanations that I looked up. I see a common thread in what was recommended as to the cause. CONTROL MODULES. PCM BCM and FPCM. But I doubt that either of these being replaced will fix all problems or even replacing all of them. I believe the problem is related to the voltages. First, you said you checked the cables and they tested/looked good. How did you test or was it a sight check? Did you check all connections at the ends for cleanliness and tight? Measured voltage drop from one end to the other? If unsure how to do that, look at a few you tube videos, not just one video.
But more than anything, What is the alternator putting out at idle and when you load it by turning things on and does the voltage regulator keep up. Your whole problem may be related to a failing alternator. These systems that don't see what they expect will sometimes try to adapt but some systems do not because to that system, it is just black and white, good or bad. Google all 4 codes and read thoroughly and look for the common thing that seems to tie them codes all together. Electrical connections, voltages and circuit resistance.
I hope this helps.
P0562 has to do with the system seeing low voltage when is below 10 volts for a long enough period of time.
P2534 has to do with problems in the ignition circuit and maybe not enough voltage for that circuit.
P2635 has to do with electrical circuit to the fuel pump.
I am shortening all explanations that I looked up. I see a common thread in what was recommended as to the cause. CONTROL MODULES. PCM BCM and FPCM. But I doubt that either of these being replaced will fix all problems or even replacing all of them. I believe the problem is related to the voltages. First, you said you checked the cables and they tested/looked good. How did you test or was it a sight check? Did you check all connections at the ends for cleanliness and tight? Measured voltage drop from one end to the other? If unsure how to do that, look at a few you tube videos, not just one video.
But more than anything, What is the alternator putting out at idle and when you load it by turning things on and does the voltage regulator keep up. Your whole problem may be related to a failing alternator. These systems that don't see what they expect will sometimes try to adapt but some systems do not because to that system, it is just black and white, good or bad. Google all 4 codes and read thoroughly and look for the common thing that seems to tie them codes all together. Electrical connections, voltages and circuit resistance.
I hope this helps.