Personally I think the power of the military in the post war climate is often overblown. That is Imo esp. so if Germany wins in some form. Yes they took more and more power in the curse of the war, but it was largely legal for them. So after the war is over Imo the civilian authorieties will most likely take back the reigns of government.
That is not to say that the military will not be influental, but that they would take over is Imo not in the cards.
As for the other questions, Germany will most likely not start a second round then, but that is not to say it could not happen, there will be loosers still and they could try for a rematch in some form.
The Great Depression had many causes but without knowlage on how Germany won, it is too open to answer that. It was ten years later in OTL so here there will be a very different world. Could something resembeling the Depression still hit? Certainly but it will most likely be different in its causes and results.
What else will happen? Write a TL and many things are possible, but with such a generalized question it is impossible to say what will happen further down the line.