P0046:
Code P0046 is set when a short to ground, open, or short to power is identified in the VGTCV or wiring between the PCM and VGTCV. This circuit is a continuously monitored circuit that takes less than 1 second to set. First thing to do is to verify that the VGT actuator is fully plugged in and that the connector and wiring are not damaged.
Sounds like you already know that. I had an issue w/ that connector and just spliced in a new one. No issues since.
P0231:
Possible causes: Open/short circuit, relay, inertia switch or fuel pump (DTC is for no voltage on the fuel pump monitor circuit)
btw - this relay is not serviceable separately - it can be serviced only with a replacement of the Central Junction Box, CJB, under the steering column
P0113:
IAT low: -40 *F. This is the code for a disconnected MAF.
P0113 and P1102 could be caused by a broken/damaged Vref wire at the Mass air flow sensor. I have seen this cause a buck/jerk and black smoke since the engine uses both sensors to control fuel, VGT position, EGR position and monitor how much EGR is flowing as well as how much fresh air is flowing. Pull up the MAF pid and IAT1 pid on your scanner and watch them very closely while you wiggle the harness right where it goes into the connector up and down and side to side. If you see any fluctuation in it while wiggling it, then you would definitely want to replace that connector with a new pigtail. The P1102 could also be caused by a boost leak, exhaust restriction, binding turbo, egr valve, or lack of proper fuel into the cylinders.
P0611:
FICM memory fault. Loss of FICM Power or internal FICM failure: FICM memory fault will set if a RAM or ROM fault exists. Loss of FICM Power. Other internal FICM failure.
P1378:
Low FICM logic power. System detects less than 7 volts. Could be low batteries, loose connections (or excessive circuit resistance), bad relay, or even a bad FICM: FICM detects logic power low, less than 7 volts. Low batteries, loose connections/ resistance in circuit, defective relay.
B1676:
Battery Voltage Out of Range EATC Module, Battery Voltage Out of Range DSM, Supply Voltage Out of Range ABS
Sounds like the FICM may need to be rebuilt and I would definitely load test each battery individually.
Check MAF (IAT1) wiring, and resolve the vgt wiring issue.
Unfortunately the fuel pump issue might be a pain. You can get a new fuel pump without buying the entire HFCM. That isn't the issue. The issue is that it sounds like you might need a new CJB, central junction box.