I would say it does, but, unless someone manages to dig up Imperial Mint records, we're never going to have any actual evidence that happened.
No, not really. Every emperor wanted circulation coins to bear his image. However, there are documented special issues amongst ancients that were only made for presentation to dignitaries. If that is a definition of a proof ancients have them. Doug's definition you can tell was written after the advent of machine striking. I do not see the necessity of most of it. To me, a proof is simply the intentional "perfect" coin capable of being struck at that point in time.
The Petition Crown was created in 1663 by Thomas Simon as an example he believed would be superior to his competitors for the coining contract's work. It is graded by Spink UK as Good Extra Fine(British Grading) but is likely the earliest proof as we know it.
Despite the context of the modern definition of a proof, I'd think that an "ideal die" would still apply to each method of coinage (e.g. press, hammer, stamp, etc.). I can picture this guy below who's tasked with creating a new design by chiseling an ideal die with the most immaculate design, using the most perfect planchet, and hammering it multiple times and then some for good measure (you wouldn't want to risk starting all over if you prematurely lift the die off and hammering to find that you double-striked an expensive and perfect planchet).
Here, maybe? https://books.google.com/books?id=12AGAAAAQAAJ&printsec=frontcover#v=onepage&q&f=false Page 28 mentions Proofs for Cromwell, although from the context it appears to carry the older, "design for approval" connotation of "Proof."