Thanks for the report David.
It sounds like you a reporting two different issues: tree menu behavior and keyboard hotkey behavior.
For the tree: right now menu in the tree only refers to the element you right-clicked on, not to the selection. So you can, for example, right-click and select "duplicate" for an element even if you have no elements selected (or a different one, or multiple elements).
This was a deliberate decision on our part because sometimes you want to mess around with elements on via tree without having to select them first.
For the hotkey: I'll need to think through the implications of allowing duplication w/ a multiselection.
One potential issue I can think of right now is what people expect when one element of the multiselection cannot be duplicated. Say you have three things selected: A, B, C. If C cannot be duplicated for some reason, would you rather have A and B duplicate, or no action to occur?