UPDATE I have found a definitive answer to at least the first part, thanks to Steven J Flebbe on Patreon. This comes from German Tanks In World War Two In Action by George Forty, former director of the Bovington Tank Museum.
The first 20 Panthers to come off the production line at MAN from November 1942 onwards were designated Ausf A in the normal manner, although as we shall see, this designation was later changed. The Ausf B was to have been a version to be fitted with the Maybach-Olvar gearbox instead of the specially-designed ZFAK 7-200, but this proved abortive and the designation was never used. It could be said that the original 20 Ausf As were really pre-production models as they did not have any of the design improvements which had been proposed following the pilot model trials... What happened to the designation Ausf C remains a mystery, but it was presumably allocated to another model that never left the drawing board, so the first full production model was designated Ausf D. To try to keep the records straight the Ausf A batch was later given the designation Ausf D1, while the Ausf D was sometimes called Ausf D2.
That explains why the first production models were called Ausf D.
However, no explanation for why they went back to Ausf A.
The next production model was for some reason designated as Ausf A instead of the expected Ausf E.
UPDATE I asked Curator David Willey, of The Tank Museum, and he answered in the April 2021 Patreon Q&A.
I have never found a straight answer to why the first production models are coming out as D's.
Good work, you've stumped The Tank Museum.
However, he references Germany's Panther Tank by Thomas Jentz (the same mentioned by Marakai) to offer a theory. Unlike American A, B, C or British Mark 1, 2, 3 which designate a production number, Ausführung letters designate separate designs. If Ausführung D is ready first, that's what goes into production as Ausführung D. Furthermore, troops did not tend to refer to Ausführung letters except for repair and maintenance.
There was no particular order to the Panther's Ausführung letters. There's no evidence of a Panther Ausführung B, C, nor E ever existing. My own speculation is D stood for something like Tiger Ausf. H is for Henshel. It's not the designer, that was Maschinenfabrik Augsburg-Nürnberg (MAN).
And unlike the well-ordered US system, the German system is inconsistent over time and project.
He quotes Jentz (parenthesis are Curator Willey's interjections)...
...the Ausführung letter designation was not used when issuing Panthers to unit nor was the Ausführung used in making decisions relating to tactical employment. (Just because you've got G's and they've got A's or something makes no difference to the troops.) The original use of the Ausführung designation was for specific identification by the designers. The assembly firms also used the Ausführung designation stipulating in their contracts the delivery of a specified number of each Ausführung. As used by the troops the Ausführung designation was used to identify compatible repair parts and identification of differences to aid in maintenance. The original records do not contain a single reference to an Ausführung B, C, or E nor is it a logical assumption that these three letters were ever used. The Ausführung letter was a modifier applied to the designation "PzK Panther".
Curator Willey goes on to explain...
...what I think he's really trying to say is that actually as a Ausführung it's a specific set of drawings for a model. Not necessarily we always start with this model A, model B. And if the model as we think the model D is kind of been worked up and is ready ahead of what we might have logically said was an A... then that is the one that is chosen and why it's going into production that way.
This is my own speculation before I heard from Curator Willey.
Once you start looking into wartime German model names you realize it's a big mess.
David Willey, curator of The Tank Museum, mentions this in Tank Chats #16.
The actual first model is not Ausführung A, the model A, as we normally would consider them. They work down the letters in the German system. The first model that goes into production is actually the model D.
Obviously this contradicts how earlier Panzer models go, like the Panzer IV going from A to J. Those were all pre-war designs. Perhaps this is a wartime change, though I can't imagine why.
This also doesn't explain why they started with D, and why there's a later Ausf. F and G. Unless they hit A and had to start again from the top. Seems pretty short sighted to start with D.
When we look into the Tiger tanks we also see a mess. The Tiger I started out as PzKpfw VI Ausf H1, H for Henschel, the designer, in contrast to Porche's competing prototype. It's possible Panther began with Ausf D for Daimler whose prototype was considered superior, but Hitler chose the MAN design instead.
By the end of the war the Tiger I was PzKpfw Tiger Ausf E. While the Tiger II was PzKpfw Tiger Ausf B. They're both models of PzKpfw Tiger but in reality they are totally different tanks.
To add to the confusion, Tiger I began as SdKfz 182, but was later retroactively changed to SdKfz 181 when the Tiger II became SdKfz 182.
I've seen several references to an order by Hitler on 27 Feb 1944 to change PzKpfw VI to PzKpfw Tiger and PzKpfw V to PzKpfw Panther. This may account for the change in model numbers. But I've been unable to find this order.
My educated guess is they started with a simple, orderly pre-war system (PzKpfw I, II, III... Ausf A, B, C...) which broke down in the increasing chaos of wartime production, competing industrial concerns, and ego stroking. They started making it up as they went along (the first Tiger is not Ausf A but Ausf H for Henschel) then had to retroactively deal with the consequences (I guess we'll count backwards), and every once in a while Hitler throws a spanner into the works (it's not the PzKpfw VI it's the PzKpfw Tiger, and this utterly new tank over here is also PzKpfw Tiger). By the time Panther comes around in 1943 this mess has stuck.
UPDATE Nicholas Moran "The Chieftain" fielded this in his Q&A #10 @ 55:11.
As for why D than A, technically A then D then A, there are multiple theories, none of which with any documentary evidence behind them. So your guess is as good as mine.