Actually, the framed photographs were purchased by Parmigiani Fleurier, and one of them was offered to you as a gift from them. The photograph is a limited edition of 10 pieces in this size, and yours is 1/10.
the fusee looks like the second diagram you made. But as is typical of Lange, the spring is never low quality, and always the highest quality. Nevertheless, the calculation is complex but not rocket science.