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These may be separate issues here.
If the fuel pump is still dying out even after it was replaced I would check the black ground wire from the pump where it bolts to the frame and see if it is loose or corroded needing cleaned or replaced as this can cause this fault here.
As for the stabilitrak and tire monitor light this may be a faulty wheel speed sensor sending an incorrect signal on what speeds one of the wheels is rotating at.This can cut back on vehicle power when this occurs.This needs checked reading the sensor values while driving the vehicle to see if one needs replaced.
The issue with the transmission is usually a faulty with debris build up in the valve body needing a transmission flush done to correct this or an issue with the valve body itself in some cases needing replaced.
I would have these checked into further here to see if any are found to be at fault needing repaired/replaced for this issue.
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