In the spectrum, are different frequencies correspond to the points on concentric circles centering on the center of the spectrum image? (e.g., the center of the spectrum means 0 frequency, and the further the point is from the center, the higher the frequency)

Also, how does the position of the point in the original image correspond to that in the spectrum image?

When only a single point in the original (left) image has a non-zero value, then the spectrum on the right will appear all white. This is because the Fourier transform of a Dirac delta impulse function \delta(x-x_0,y-y_0) at position (x_0,y_0) is given by \exp^{-2\pi i (x_0 fx + y_0 fy)} (i.e., it's magnitude is 1). Similarly, when one point in the right image has a non-zero value, the inverse Fourier transform is \exp^{2\pi i (fx_0 x + fy_0 y)}.

Consider now the relationship between different points on concentric circles in the right image, and their inverse Fourier transforms. The inverse Fourier transform of each point is \exp^{2\pi i (fx x + fy y)}, where \sqrt{fx^2 + fy^2} = f is fixed. These are just rotated versions of the same function! So one can think of the points on a concentric circle as representing different orientations of the same frequency f.

Quiz 4 also provides some good information on this.