Yes, while dragging press Alt once (do not hold it down). You should see a little "+" sign show up near the cursor, that means it will make a copy. Also check out the Gumball manipulator.
No, not in that way. Objects do not have parametric properties in Rhino, they have no "memory" of the numbers that were used to create them. So you will have to post-edit the objects differently. For example with sub-object selection you can move one of the faces of your cube by dragging or a specific distance move (with or without Gumball). All the usual transformation tools such as scale, rotate can also be applied to sub-objects.