–The group isn’t showing in the Outliner…
In the outliner window you need to change to Groups in the dropdown list.
–When scaling, grabbing or rotating, why doesn’t the entire group respond as one piece?
Select the whole group or you may want to look at parenting/child relationships rather then groups
I’m a bit frustrated that there doesn’t seem to be an advantage to grouping objects in Blender.
From the wiki:
Use groups to just logically organize your scene, or to facilitate one-step appending or linking between files or across scenes. Objects that are part of a group always shows as light green when selected; see image (Grouped objects). You can mix any kind of objects in a same group.
Grouped objects are also used in object duplication in dupligroups or in particle systems