What is the smallest size wheel I'll get over the brakes?
Assuming the MK7 GTD has stock brakes with 312mm discs the smallest wheel you can theoretically fit are 16" though it will be a squeeze. 17" would be a safer bet but what really matters is the clearance from the brakes and strut (offset) and the design of the spokes.
I generally use
Willtheyfit to get a rough idea of how much poke you need to clear the strut and brakes from your existing setup, it helped me gauge an idea of what OEM wheel I need to fit over my Porsche Boxster brakes.
What Rim size will I need?
5x112 bolt patterned 16x6.5+ / 17x7+ wheels mainly but again offset is the key factor here. Use the calculator to see how much inwards/poke the new wheel setup will be.
What Tyre size would I need to keep the speedo reading right?
205/55/16 or 225/45/17 are standard OEM tyre sizes and will be within <1% margin of error from the speedo.