So that has solved your original problem. i.e. Mega2560 + Adapter + 3.2 inch (40-pin)
No. Straight male header strip is not long enough to bend. Buy ready-made angle header. Local Ebay or Main Distributor will have this in stock. Or ask the University Laboratory staff.
There are two GND pins on the 2x18. There are two 5V pins on the 2x18.
It may be a University project. I would try to make it robust but the most important thing is your "7 days left to complete the project"
For a practical device to use in a real car I would want to assemble with mating pcbs and soldered joints. e.g. with Protoshield or Protoboard.
Seriously. Look at the pinout diagrams for Mega2560 and Due. Think carefully about which pins you have available and how easy it is to connect external electronics.
David.