Question

[Q] How to use Fisher’s Z-transformation to compare Correlation Coefficients?

Answer 1

It is not totally clear to me what you are correlating, but assuming your associations are dependent, you might want to check out the "cocor" function in the "cocor" package in R. It can compare two correlations based on either dependent or independent groups. You can find the documentation on CRAN.

Answer 2

If the correlations have been converted to Z's, you simply test the difference of the Z's.