Buying a Speedy reduced 3510.50.00, but is it fake?

Looks perfectly genuine. Can you show examples of fakes since I have never seen a convincing fake of one of these. They use a compound movement which is difficult to fake in many ways so as long as the pushers and crown are out of line any you see that looks right is prob legit. The casebacks varied over the years from very plain with text only to ornate like you show above. Some early ones have the serial only inked onto the inner caseback which can wear off during cleaning so have no serial at all in effect. Some have it on the lug and others on the outer caseback. There were also 4 different movement numbers I recall and different movement finishes used over the life of the model which ran from around 1988 to 2006 or so. It's complicated!

See what I said about the 4 movements used above, you show 2 of the variants there, the first, the 1140 and the last the 3220. They made this model for nearly 20 years don't forget, there were changes.