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As the USSR no longer exists as a sovereign state all countries are free from it.
Generally, yes.
Communist
The former USSR, headed by Russia, were communist countries. Most of the outlying territories were taken by force and unwillingly converted to communist governments.
China is a communist country. The cold war was between the western countries and the communist countries. China supported the communist countries.
Eastern European countries became communist, which was a political ideology modernized by the USSR.
China and the USSR
Hungary is not communist. They were before the fall of USSR. They are now democratic, but are slowly moving toward the right-wing as Jobbik has gained enough power in the government to be able to change it.
Communism has no classes or borders or states and will have to exist at a global level, so there can be no such thing as a Communist country. USSR, Cuba etc were state capitalist.
All countries in Europe expect USSR, Romania, Poland, Bulgaria, Albania, Hungary, Czechoslovakia and East Germany were NOT communist.
The main issues were the economy and the Communist threat including a perceived "missile gap" with the USSR and the Communist government of Cuba. Kennedy promised to fix both.
The USSR did not change after World War 2 but they did possess the Eastern European Nations they conquered when they defeated the Nazis. They remained a communist country until the early 1990s.