"That's exactly what happened. The US switched from a policy of ousting Castro and his merry band of Communists from Cuba to a policy of getting rid of missiles. If memory serves, we even agreed to remove our own missiles from Turkey as part of the exchange. In short, Kennedy's "standoff" with the Soviets was an unmitigated disaster for the US, not to mention Cubans suffering under the jackboot of Communism. Moreover, once Castro secured our blessing to establish a permanent Communist beachhead 90 miles from the shores of the US, he immediately sprang into action and began fomenting Communist revolution both in the US (Black Panthers, Weather Underground, SDS, etc) and throughout Latin America."
The Soviets thought they could put the missiles on Cuba because they thought Kennedy a naive indecisive president -based on his poor performance during a "summit" with Khrushev early in his presidency. They were mistaken. They did not expect the response of the US. The missiles in Turkey were slated to be removed prior to the Cuban missile crisis. All the Soviets "got" was the removal of missiles that we had already promised to remove. The Cuban Missile Crisis was a success for the US. The unmitigated failure of the US was earlier during the Bay of Pigs - another example of Kennedy's indecisiveness to the Soviets and probably helped encourage their decision to take such a provocative step such as basing missiles on Cuba.
Most of the groups you mentioned above were more-than-likely funded by the Soviets and via the World Peace Committee. Castro naturally more-than-likely assisted. He's pretty p.o.'d at the Russians now.