Christine,
> 1) For a given region of interest, how do I obtain the correlation coefficient for each of the effects?
See here: [
afni.nimh.nih.gov]
> 2) For the unmodulated effect, does that mean that those are voxels where activity was equal
> (i.e., not different) across all trials of interest?
By "unmodulated effect" I assume that you mean the first effect estimate in the output for each set of modulation analysis. If so, the phrase "unmodulated effect" is misleading: just as the intercept of a linear model, the first beta value is actually the effect that is associated with the mean value (or center) of each modulation variable.
Gang