By design the drag in FileExplorer is allowed only when dragging items from the Grid to the TreeView and no vice versa.
As for the renaming - there is slight difference of the command behavior in both panes which might be misleading you. When renaming a folder from the TreeView (left pane) no "Rename" pop-up is shown, but the renaming is done inline in the node. You can see the described behavior here: video
. Note that you will be able to rename a folder in the TreeView only if its parent folder has been provided with enough permissions.
I hope this explanation will shed some light on the subject.