Short answers, pulled from the story.
The Rapacki Plan was a proposal for a nuclear-free zone in Central Europe, presented by Polish Foreign Minister Adam Rapacki to the United Nations General Assembly on the 2nd of October 1957. It called on Poland, East Germany, West Germany, and Czechoslovakia to ban the production and storage of nuclear weapons on their territories.
NATO rejected the Rapacki Plan at a council meeting in Paris in December 1957, arguing that removing nuclear weapons from Central Europe would leave Western Europe vulnerable to Soviet conventional armies, which the alliance considered the greater military threat. West Germany was also strongly opposed because accepting the plan would have required signing a treaty with East Germany, violating the Hallstein Doctrine.
Adam Rapacki, Poland's Minister of Foreign Affairs from 1956 to 1968, presented the plan and gave it his name. Przemyslaw Ogrodzynski, Director-General of the Ministry of Foreign Affairs, is credited as one of its principal architects, working alongside Manfred Lachs and Henryk Birecki. Polish leader Wladyslaw Gomulka provided the political backing that enabled the proposal to go forward.
Yes. The Soviet Union supported the plan, seeing it as a way to prevent West Germany from acquiring nuclear weapons and to restore Soviet prestige after international condemnation of the suppression of the 1956 Hungarian Uprising. On the 21st of December 1957, the Supreme Soviet passed a resolution endorsing it, and Nikita Khrushchev publicly called for an "atom-free zone" in Europe at the Twenty-First Party Congress in March 1958.
The Eisenhower administration opposed the plan, arguing it would benefit the Soviet Union by removing American nuclear weapons from West Germany and upsetting the balance of power in Europe. Secretary of State John Foster Dulles spoke against it at a press conference on the 10th of January 1958, and on the 3rd of May 1958, US Ambassador Jacob D. Beam delivered a formal rejection to Poland.
Scholars argue that the Rapacki Plan and its successor, the Gomulka Plan proposed in December 1963, contributed to the broader Cold War dialogue on nuclear restraint. That discussion eventually fed into the Nuclear Non-Proliferation Treaty of 1968 and the Conventional Forces in Europe Treaty of 1990.