Codes P1731, P1732, U0418 and U0456, "Transmission Fault" error light on dash?

It appears that person never returned to let us know what was found. Unfortunately, that is common.
P1731 and P1732 are pretty much the same code just for two of the four shift sensors. The U0418 is a can code for the same sensor module, telling you there is a fault in the PDK system, while the U0456 is a code related to the HVAC controller, namely a com fault with it.
As you have access to PIWIS you should be able to test the sensors through it. They basically tell the PDK module the position of the shift forks as they move. With that software you should be able to watch the sensors change as the transmission shifts. If there is no change in the sensor signals as it shifts, then I would first check the harness connection for transmission fluid. The sensor assembly does have a known failure pattern related to the wiring inside the transmission failing and lubricant wicking through the wiring.
A common result of these codes is the loss of reverse gear as the PDK controller can't tell if it has shifted out of a forward gear. If you still have reverse, then the code is likely from a failing PDK module. However, you might use the tool to do a reset and with the car in park reset the shift module. See if the system clears the fault. If they take a while to return, then it's possible the sensor module is failing.

So, if you put the car in reverse does the reverse lights work? If so then the Transmission Gear Selector Switch might be okay, if not I would change out the gear selector switch, if all of these codes came up at one then chances are the TCM has gone bad.

P1731 - Transmission Control Module (TCM) Gear Shift Lock Solenoid
P1732 - Transmission Gear Selector Switch
U0456 - Invalid Data Received From Transmission Control Module (TCM)
U0418 - Invalid Data Received From Brake System Control Module

Here is how to change the switch out and the TCM in case you need it. I would check the fuses#10 and #16 in the fuse panel in the left front, this guide can help:

https://www.2carpros.com/articles/how-to-check-a-car-fuse

Check out the images (below). Please upload pictures or videos in your response of any problems so we can see what to help you with.

Yes, the TCM can be the problem. I don't think the VSS will cause these codes, did you check the fuses I mentioned above? They don't give a price but at the dealer it should cost about $1,200.00. I would call for an estimate to be sure.

Okay, this leaves the TCM or the transmission. In the service dep at the dealer would just plug a TCM in to see if it fixes it and if not do the transmission. They have this advantage.

I am sorry, they did not get back to us with a solution but I would say the TCM was the problem.