These are Bezirkshandstempelaufdrucke stamps. In English they are known as HOPs (Hand Overprints). They were issued by the Soviet Union on June 24, 1948 and were valid for postage until July 10, 1948. Because they were issued by 766 different post offices there is a lot of variety, even from the same post office.
As you have noted, there are a lot of overprint forgeries. This area is one of several difficult areas in German philately.
Literature about the overprints are available:

I don't know if the literature discusses forgeries; it may just be the history.
I have thousands of these overprints; only a few are signed. I assume the rest are fakes.