Hmm. Many of those commands are contextual. So, for example in the Edit menu a document that’s been opened in its own window but has no selected text will have such items as cut or delete grayed out. But if you select something, Cut and Delete will become available commands. And under the Data menu items most of the commands would normally be grayed out, including Duplicate, Replicate and others.
But if that document is selected in the Names column, other commands should appear, such as Delete, Duplicate, Replicate. Show in Finder would be grayed out unless the item were Index captured. And of course Cut would be grayed out unless a selection had been made.
In fact, if the focus isn’t on the document window in the Three Panes view, almost all the Edit commands are grayed out, including Paste.
So the normal operation of available commands under the Edit and Data menus will vary depending on whether the document is being viewed in the text pane of a view window (and also whether the focus is in that pane), or the document has been opened in its own window. Under the Edit menu commands will vary depending on whether or not a selection has been made.
That said, if you click on the Name of a document in Vertical Split, Horizontal Split or Three Panes views, the Data menu should allow you to Duplicate, Replicate or Delete it, for example.
If that’s not the case, something is wrong. Try the obvious first. Quit and relaunch DT Pro, or even better restart your computer to sweep out any cobwebs in memory.