From: Bedfordshire UK
In answer to your specific questions
That may apply to the German side, but the Soviets may have attacked in blizzard turns. If you apply this as Soviets, you may not be able to attack during much of the winter and there will be little Soviet winter offensive.
The supply level is set by the game, it depends on distance from HQ and enemy control of surrounding hexes (not necessarily where the enemy units end their move).
Some house rules forbid 'Supply Mules' (empty HQs established only to provide extra supply), but to my mind, I see no problem in taking supplies from where-ever you can get them. I don't use empty HQs, but if one normal HQ has more supply than it needs, or an emergency occurs with another HQ, I see no problem in stealing supplies. Patton and Guderian would have done that and surely any High Command would order an HQ to release unneeded supplies to another HQ, under greater threat.
Not sure if mid-game save affects AI games, but Alt-R command saves a status report into your WIR folder (looks like GE050743.txt - e.g. German side with turn date 5/7/43). You can check, or print this report, to see any changes after a save (it will over-write if you do it twice in the same turn, so save under a different name before you use the command again). The report gives a huge amount of information on the status of your units, equipment and pool lists, very useful during the game to see how you forces are faring.