The MMI system will work/startup without a control panel, it just you won't have any control over the MMI system, that was never going to be the fault with your system.

If the gateway is dead then the hole car is dead, as every module communicates vi the can-gateway, and the gateway is also located behind the glovebox.

Gateway is the one with the VW/Audi logo in the picture below, and you can see the two optical cables going into the unit.

All the other part locations are correct in your list