All children located in a group take the property values set by the parent (group). This answers both your first and last request.
For the first - Add multiple objects into a group within the Hierarchy and move the group node. All the children of the group should follow.
For changing multiple properties, it’s very similar to the above example. Adding an object (or multiple) into a group would allow all properties to be overridden. For example, if a group’s color property was to be changed, so would all the planes within that group.
We have some basic Keyboard Shortcuts in Studio but none to duplicate objects directly in the Hierarchy. This could be a great addition!
Hope this helps,