You can do that now, after a fashion. Make yourself a context mode perspective that shows completed actions, grouping by date completed, probably sorting by project or date completed, completed actions with all the groups closed except completed today (or whatever you need to show). Save it as a perspective, with the Restore Expansion box checked.
You can do the same for items added by grouping by date added, showing all actions. If you've got a lot of repeating tasks, the usefulness of this perspective is diminished.
I assume by deleted you mean completed; there isn't a practical way to keep track of items you've actually removed from the database.
RobTrew's excellent Where in OF
script will let you do all sorts of wondrous searches (need to see actions with "xyz" in the notes field that were completed last Thursday, added before January 13, 2012 and were estimated to take at most 15 minutes? You can do it!) but it does not give you a display showing *only* those items (you may have to see other actions in the display, though the searched-for ones will be the only ones highlighted by selection, so you could copy and paste into some other document), and the display is static.