What events in soviet history (1945-62) might kennedy have been referring to when he said that the U

desire to conquer other nations?

What events in soviet history (1945-62) might kennedy have been referring to when he said that the USA had no?chinese theater

I would think it is referring to the Bay of Pigs invasion that the USA had sponsored by arming the rebels, and sending them to what was to be their slaughter. Kennedy refused to give the invaders the air support promised.

What events in soviet history (1945-62) might kennedy have been referring to when he said that the USA had no?opera mini opera theater

At the end of WW2, The US and it's allies, returned to civilain control all the countries it had occupied while fighting the Germans and Japanese. They did not take them over.

The Soviets, on the other hand, stayed in Eastern Europe, North Korea, and tipped the balance in China. They ousted or executed local leaders, and installed puppet governments which answered only to them.
After WWII the Soviet Union had engulfed the formerly independent Baltic nations like Latvia, Lithuania and Estonia as "Soviet" republics under Moscow. Also, the governments of Poland, Czechoslovakia, Romania, Hungary and East Germany and Bulgaria were given by the Soviets to communists who were more loyal to Moscow than to their own countries. The Soviet troops based on those countries had the power over the local armies and could be used and were used against the local people even over the dictates of the local leader. They were in fact, colonies. It has been anrgued that the western democracies were US colonies as well, the difference is clear. In France, Italy, Britain, amongst others there were and I believe, are, communist parties with a legal activity. In a colony, that would not have been possible.