Short answers, pulled from the story.
The Soviet empire refers to the territories the Soviet Union dominated politically, economically, and militarily during the Cold War, despite the USSR officially declaring itself anti-imperialist. Scholars apply the term because the Soviet Union exhibited tendencies common to historic empires, including military intervention, colonialism, and control over nominally independent states.
The Warsaw Pact included Albania (1946-1968), Bulgaria (1946-1990), Czechoslovakia (1948-1990), East Germany (1949-1990), Hungary (1949-1989), Poland (1947-1989), and Romania (1947-1965), alongside the Soviet Union itself. These states were also members of Comecon, the Soviet-led economic community founded in 1949.
Major Soviet military interventions occurred in East Germany in 1953, Hungary in 1956, Czechoslovakia in 1968, Poland in 1980-81, and Afghanistan from 1979 to 1989. These interventions enforced the limits Moscow set on the domestic and foreign policies of nominally independent countries.
Sovietization was the imposition of Soviet-style political, economic, and cultural systems on territories dominated by the USSR. It involved installing Soviet-controlled governments, removing opposition candidates from elections, nationalizing land and property, repressing class enemies, and using mass deportations, Gulag imprisonment, and propaganda to enforce conformity.
The Brezhnev Doctrine was the Soviet policy permitting the invasion of other socialist countries to prevent them from leaving the Soviet orbit. Mikhail Gorbachev formally relinquished the doctrine in 1989, which accelerated the collapse of Soviet influence over the Eastern Bloc.
Finland was nominally neutral but constrained by the Finno-Soviet Treaty of 1948, which required Finland to defend Soviet territory from attacks through Finnish soil and effectively gave Moscow a veto over Finnish foreign policy, preventing Finland from joining NATO. This arrangement gave rise to the term Finlandization, used to describe countries that accommodated Soviet pressure without formal incorporation.