1. If your light and heavy peptides have completely different sets of transitions but you still want to normalize by dividing the total light area by the total heavy area for that peptide then you should check the "Simple precursor ratios" checkbox on the "Quantification" tab at "Settings > Peptide Settings".
However, this would be an unusual thing to want to do with peptides.
2. If you want to normalize by dividing by the area of a completely different peptide then that is a "surrogate standard". There is some information about surrogate standards here:
https://skyline.ms/wiki/home/software/Skyline/page.view?name=Surrogate%20Standards
3. I am pretty sure that the normalization method that you are describing where you divide first by the global standard area and then by the heavy area does not make mathematical sense. That would be similar to dividing by the square of the normalization factor, which also would not make sense.
4. As of Skyline 24.1, the value that you see in the Document Grid "Protein Abundance" is calculated by summing the transition areas. When you are customizing your report there is a different column "Protein Abundance Transition Average" which you could have on your Report instead.
You can learn more about the Document Grid and Custom Reports here:
https://skyline.ms/wiki/home/software/Skyline/page.view?name=tutorial_custom_reports
If you want to compare protein or peptide abundances between different groups of replicates (i.e. cohorts) then you should look at the Group Comparison tutorial:
https://skyline.ms/wiki/home/software/Skyline/page.view?name=tutorial_grouped
-- Nick