Difference between normalization and zero centering
what is the difference between these two steps?


In that specific Notebook that you linked, normalization means: shrink a numerical distribution in the [0,1] interval. It is commonly referred to as Min-Max Scaling. Shrinking the distribution in the [0,1] interval moves its mean somewhere between 0 and 1.

Zero-centering instead means: to "shift" the values of the distribution so that its mean is equal to 0.

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  if one normalize the image pixel values to range [0, 1], is it have a
  benefit to also do zero centering?


Zero centering variables improves ML models performance. Activation functions tend to be very responsive to weights' changes especially around zero. I found some good explanations here.

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  Is there a difference if I do normalization first or zero centering
  first?


The order matters, since "normalization" would move the mean away from zero.