Grouping

Having Issues with groups select objects functionality.

Invert select does not deselect the currently selected group!
Can I isolate selections to items of a current group ?
Can I "select all" from just within a group ?
Can I invert a selection just from within a group ?
Can I iteratively expand or collapse entries listed in a group ?
Can I array a group of objects and have that original group and all the resulting groups wind up in the same parents group?

What is the layers' relationship between groups and their constituent objects ?

Thank you for all your good work !
MindSet