Short answers, pulled from the story.
The Soviet Union conducted its first nuclear weapon test, designated RDS-1, on the 29th of August 1949, at the Semipalatinsk Test Site in Kazakhstan. The Americans code-named the test Joe 1. The device was modeled on the American Fat Man bomb and used an implosion-type design with plutonium.
Igor Kurchatov served as the technical director of the Soviet atomic bomb project, appointed in late 1942. Lavrentiy Beria, head of the NKVD, was placed in overall administrative charge of the program by Stalin on the 22nd of August 1945. The weapons design bureau at Arzamas-16 was led by Yulii Khariton.
Soviet intelligence obtained detailed technical information from Klaus Fuchs, a British physicist working on the Manhattan Project, and from American Theodore Hall, among others. Kurchatov told Molotov that the espionage materials were "magnificent" and added exactly what the program had been missing. Historian Richard Rhodes estimated the intelligence accelerated the Soviet program by a full two years.
The Soviet Union tested its first thermonuclear device, the RDS-6S, on the 12th of August 1953, producing a yield of 400 kilotons. A true two-stage thermonuclear bomb, the RDS-37, was successfully tested on the 22nd of November 1955, with a yield of 1.6 megatons. Both weapons were developed with contributions from physicist Andrei Sakharov.
The Tsar Bomba was a three-stage hydrogen bomb detonated on the 30th of October 1961 over the Novaya Zemlya archipelago. It produced a yield of approximately 50 megatons, equivalent to ten times all the explosives used in World War II combined. The device was capable of approximately 100 megatons but was deliberately reduced before the test.
The Soviet Union tested 969 nuclear devices between 1949 and 1990, more than any other nation, including 214 atmospheric tests before 1963. Testing at Semipalatinsk exposed hundreds of thousands of Kazakh citizens to radiation. Lake Karachay near the Mayak site was used as a radioactive waste dump from the early 1950s; in 1967 it dried up and winds spread radioactive dust over thousands of square kilometers, exposing at least 500,000 people.