Shape Matching using Discrete Fourier Transform

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This is the very first time messing around with DFTs so apologizes inadvance if the Math just flies over my head or my question sounds rather stupid.

Disclaimer: I have not used OpenCV API for any DFT related steps stated below

What I have done so far

Let T represent the template image and S be an image I get from the camera feed

1. Grabbed the contours from T
2. Applied DFT on them
3. Made the attained DFTs scale invariant by dividing them with their magnitude i.e. F[i] = F[i]/|F[i]|
4. Computed their magnitude spectrum
5. Log-polar transformed the magnitudes and calculated the phases i.e. angles

My questions are:

1. Just to confirm, after performing Step 2, my attained descriptors are translation invariant correct?
2. How do I make them rotation invariant?
3. Now this is where I get really confused. After reading a couple papers on image registration, Steps 4 and 5 are needed. This is in order to calculate the phase correlation then trying to maximize this value. For my application, is this really necessary? Or do I just have to make the descriptors rotation invariant then calculate the euclidean distance to the descriptors of S and trying to minimize this value my final step?

Any help/suggestions are sincerely appreciated!