FFT (DFT) of 2D Images
Consider a 1D wave of 10sec duration.

I correct in assuming that the fundamental frequency is the image itself?
Does the 10 sec sample equal the fundamental freq? No. same for images.

And one copy of the image is equivalent to 1 wave cycle?
Repeat above. Answer: No

The sampling frequency is the number of pixels in the image?
One pixel can be thought of as the sampler. But, this could be changed. You could go for sub-pixel sampling also.

With this I think the last question has no relevance. Comparing two images, to the best of my knowledge is an open ended problem.