Janelle,
> is the reason behind why dummy coding is not necessary for 3dMVM because the program can accept explanatory variables
> that are categorical (i.e., factors) in addition to explanatory variables that are quantitative?
The user does not need to dummy code categorical variables because 3dMVM (and other programs such as 3dLME and 3dLMEr) dummy code them internally.
> Would the setup below be correct for 1) modeling main effect of group, and 2) modeling this type of interaction?
It would be better to adopt one model for all of your research hypotheses. Try something like
-bsVars "Group*FatherAge+Group* BrainVolume+Site+MEdu" \
-qVars "FatherAge,BrainVolume" \
Gang