Fourier transform of 1 r in 2d

1. What is the Fourier transform of 1?
2. What is 2D Fourier transform?
3. What is 1D FFT and 2D FFT?

What is the Fourier transform of 1?

Fourier transform of 1 is unit impulse function.

What is 2D Fourier transform?

The (2D) Fourier transform is a very classical tool in image processing. It is the extension of the well known Fourier transform for signals which decomposes a signal into a sum of sinusoids. So, the Fourier transform gives information about the frequency content of the image.

What is 1D FFT and 2D FFT?

Just look at the math for 1D vs 2D FFT. In the 1D case, there is only 1 independent variable (x[n]). In 2D, there are two. It doesn't make sense to apply a 2D signal (i.e. two independent variables such as rows&columns in your image example) to a function that only takes one independent variable.