As I understand it, the KGB inherited their dirty tricks bag from the Cheka, whose members had learned them the hard way from being on the receiving end, taught by the https://en.wikipedia.org/wiki/Okhrana .
Not really. The USSR did not allow any members of the Imperial police to join the USSR secret service (it was initially called OGPU).
They also functioned quite differently, the Imperial security had never had a fraction of OGPU's power, so the methods were different. OGPU didn't care at all about planting evidence or manipulating witnesses, they could just torture people into signing confessions (called "the queen of all kinds of evidence" by the USSR chief prosecutor).
So any similarities are probably just a result of parallel evolution.
