Thank you again for your time, GB.
I set up individual Apple ID's for my children so that they could have their own Apple ID on their individual iPad minis (gifts from grandparents last year). When I go to iCloud under Settings, I see my Apple ID listed at the top, then my children's listed under Family Sharing. So the device is still using my Apple ID for iCloud, iTunes, etc., correct?
To "assign" their own Apple ID to their own iPad mini, I would need to "Sign Out" from my Apple ID. When I attempt to do so, I receive a warning that all of the Documents and Data will be lost/deleted.
So, instead of doing this, I figured out that I could do what you suggested. Signing in using a child's Apple ID will allow her/him to use Game Center, FaceTime, and Messages just fine. However, using their Apple ID for iTunes & App Store proved to be a problem: Purchased Music and Movies appeared in iTunes, but my Purchased Apps did not appear. Some Apps even disappeared, e.g. Proloquo4Text (a $99 app to help my son speak with his iPad).
So I reverted to using my Apple ID for iTunes & App Store, and I get everything that I want, EXCEPT for the iCloud storage for each Apple ID.
So that's when I started wondering how Family Sharing was really benefiting me ~ It was a lot of work (deleting apps to allow space to download iOS 8, etc) without any benefit that I can see. UNLESS I find a means to allow me to sign in each iPad's iCloud account with a different AppleID, then perhaps restore the Documents and Data from a backup? Would that work?
Thanks.