Also, I'm unable to change the Style color or change the visibility on object outlines for objects that are grouped as a whole, not without drill-selecting into the group or Ungrouping the set. A feature?

[ah... you can change the Style if you select the yellow dot for each individual sub-object. When you change the style of the whole group object, the Style swatch up top says that it has the new color, but the objects themselves remain unchanged.]