Short answers, pulled from the story.
The Czechoslovak Socialist Republic officially began on the 10th of December 1989 when the country transitioned back into democracy through the Velvet Revolution. The state existed from 1948 until its final dissolution on the 1st of January 1993.
Alexander Dubček served as First Secretary from the 5th of January 1968 until the 17th of April 1969. His liberalization reforms were stopped by a joint invasion of the Soviet Union and Warsaw Pact forces on the 20th and the 21st of August 1968.
Rudolf Slánský and eleven others were convicted together of being Trotskyist-zionist-titoist-bourgeois-nationalist traitors. They were executed after their conviction, and their ashes were mixed with material used to fill roads on the outskirts of Prague.
The economy operated as a centrally planned command system similar to that of the Soviet Union where producer goods were favored over consumer goods resulting in shortages of quantity and quality. Economic growth rates lagged well behind Czechoslovakia's western European counterparts despite high economic growth averaging 7% per year in the 1950s.
The official name changed from the Czechoslovak Republic to the Czechoslovak Socialist Republic when the 1960 Constitution of Czechoslovakia was promulgated on the 11th of July 1960. This act codified the actual state of affairs that had existed since the 1948 coup.