Dear Alfonso and CONN experts

I have a question regarding using separate covariates for each group in a between group comparison, and despite the numerous messages on this topic I am still debating. I have two groups – men and women- and I want to include their total GM as a covariate in second level ROI-ROI between group analysis. I thought that including a separate covariate for each group is better since it allows for possible group by covariate interactions (though I am not interested to test this interaction).
I created three covariates: GM_all (scores for all subjects), GM_women (scores only for women and zeros for men) and GM_men (scores only for men and zeros for women).
I have 2 questions:
1) Do I need to mean-center the scores in the group specific covariates (that is center the scores of the women in GM_women)? I thought that because the scores of the second group (men) are zeroes in this covariate I should not mean-center the scores of the women, because then I will have 2 zero scores with different interpretations, but I am not entirely sure and will appreciate your help.
2) Surprisingly, when controlling for GM as a single covariate for all subjects: "men" "women" "GM_all" and applying the contrast: [1 -1 0] and alternatively when controlling for GM by including the 2 separate covariates for each group (not centered): "men" "women" "GM_men" "GM_women" and applying the contrast: [1 -1 0 0] the results are entirely different. Any thoughts? Is this related to the centering of covariates?

Many thanks for your help and thoughts