Short answers, pulled from the story.
The PPD-40 was designed by Vasily Degtyaryov, a Soviet arms designer. Degtyaryov originally designed the PPD in 1934, and the PPD-40 was a modified version introduced in 1940 with changes aimed at easier manufacture.
The PPD-40 fired the 7.62x25mm Tokarev pistol cartridge. That round was based on the 7.63x25mm Mauser cartridge used in the Mauser C96 pistol.
The PPD-40 was replaced because it was too labour- and resource-intensive to produce at scale, with most metal components made by milling. The PPSh-41, designed by Georgy Shpagin, used stamped metal parts and a muzzle climb compensator, making it cheaper and more accurate. By the end of 1941 the PPSh-41 was officially adopted in its place.
81,118 PPD-40s were produced in 1940, the year mass production began. By contrast, only 5,868 PPDs were made in 1941 as the PPSh-41 took over production capacity.
German forces designated captured PPD-34/38 models the MP.715(r) and captured PPD-40s the MP.716(r), incorporating them into Wehrmacht inventory under standard Maschinenpistole labelling.
Finnish forces kept PPDs captured during the Winter War and Continuation War in reserve service until approximately 1960. They were issued to coastal and home guard troops.