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.
Sure the Tsarist regime was very brutal and oppressive however it still had a somewhat functioning and somewhat independent judicial system (of course extrajudicial murder/executions still occurred quite frequently but not even remotely as frequently as in the USSR).
But more importantly in this case Nicholas didn’t have nearly as much direct power as Stalin did (he was extremely incompetent as outright stupid as a person) and had to rely on his government to actually make the tough decisions.
Vladimir Korolenko described it pretty well in "Everyday Phenomenon" (1910), and "Features of Military Justice".