So if I want to use the study-specific "average" subject surface with mri_surf2surf, rather than the generic "fsaverage" one, how can this be done given that the required ls.white file only exists in the latter but not in the former? Can I just rename (or duplicate) ls.white into ls.white_avg?

You can copy it or create a symbolic link.

So it is OK to copy the required lh.white file from the generic average subject "fsaverage" and apply mri_surf2surf upon the study-specific average subject ("average")? It still seems to me that "average" should have its own (different) lh.white...

Shouldn't the input to mri_glmfit be the output of mri_surf2surf? In the group tutorial, the former is "lh.gender_age.thickness.10.mgh" while the latter is "lh.gender_age.thickness.10B.mgh". Or should it just be the unsmoothed output of mris_preproc?

Yes, I can't remember why I put the "B" there, maybe to keep people from overwriting lh.gender_age.thickness.10.mgh during the tutorial and having to wait the 10min or so for it to get recreated.

But if all these commands transform the same file (output of mris_preproc becomes input of mri_surf2surf, which then feeds into mri_glmfit), then why is it still necessary to keep intact the original lh.gender_age.thickness.10.mgh, when all you need for the group analysis is the mri_surf2surf'd version?

Assuming the label files (corresponding to my ROI, and extracted from the Destrieux atlas) are different for each subject, and given mri_glmfit is called just once, for all subjects, which label file (corresponding to what subject) should I point it to?

You need to create the label in the average subject. There is a Destrieux atlas there.

Again, by "average subject" do you mean here the generic one (fsaverage) or the study-specific one (average)? Should the former be used at any point of a group analysis, if the latter exists?