Short answers, pulled from the story.
The John Birch Society was founded on the 9th of December 1958, in Indianapolis, Indiana. It was established by Robert W. Welch Jr., a retired candy manufacturer from Belmont, Massachusetts, at the conclusion of a two-day meeting of twelve people.
John Birch was an American Baptist missionary who went to China in 1940 and became a U.S. Army intelligence officer under Brigadier General Claire Lee Chennault. He was killed on the 24th of August 1945, nine days after Japan's surrender, when Chinese Communist forces shot him after he refused to surrender his sidearm. Welch named his organization after Birch, calling him the first American casualty of the Cold War.
The JBS held that a conspiratorial group of internationalists, bankers, and politicians controlled both the U.S. and Soviet governments, with the goal of creating a one-world socialist government. It promoted Americanism as the philosophical antithesis of Communism, argued that the U.S. is a republic not a democracy, and supported states' rights over federal power, opposition to the United Nations, and the gold standard for currency.
JBS membership peaked in 1965 or 1966 at an estimated 100,000 members. By 1976 the organization had 90,000 members, 240 paid staffers, and a seven-million-dollar annual budget according to a paper by Charles Koch. By the mid-1990s, following Welch's death and the Cold War's end, membership had declined to an estimated 15,000 to 20,000.
Buckley called Welch's accusations that President Eisenhower was a Communist agent paranoid and idiotic libels. He tried and failed to purge Welch from the society, and his biographer John B. Judis wrote that Buckley feared the rapidly growing JBS could push the American right toward an ugly, even Fascist turn rather than the kind of conservatism National Review had promoted.
The case was Gertz v. Robert Welch, Inc., stemming from the JBS magazine American Opinion falsely accusing Chicago lawyer Elmer Gertz of being part of a Communist conspiracy. The Supreme Court ruled that a private figure does not need to prove actual malice to recover actual damages from a media defendant, a standard that still governs American libel law. Gertz prevailed at retrial.