Short answers, pulled from the story.
The KGB was formed in March 1954 under Ivan Serov, following restructuring in the Soviet security services after the fall of Lavrentiy Beria. It was officially dissolved on the 3rd of December 1991, after the failed August coup against Mikhail Gorbachev.
The KGB carried out foreign intelligence, counter-intelligence, internal security, secret police functions, border protection, and combating political dissent within Soviet society. It also guarded Soviet leadership and protected government communications.
FBI counterspy Robert Hanssen worked for the KGB from 1979 to 2001, while CIA officer Aldrich Ames was active from 1985 to 1994. US Navy Chief Warrant Officer John Anthony Walker was recruited in 1967 and over eighteen years helped the Soviets decipher approximately one million US Navy messages.
Before the Red Army invaded, the KGB infiltrated Czechoslovakia with illegal residents posing as Western tourists. They were tasked with cultivating sources close to Alexander Dubcek's government, planting fabricated evidence to justify the invasion, and preparing hardline loyalists such as Alois Indra and Vasil Skultety to take power.
The KGB dissolved on the 3rd of December 1991 into several immediate successor bodies, including the Federal Security Agency of the RSFSR and the Central Intelligence Service. By 1993 these consolidated into the Federal Counterintelligence Service, which became the FSB. The foreign intelligence function passed to the SVR.
KGB illegal residents assumed elaborate false identities, either borrowing the identity of a living accomplice or building a legend around a dead person. An agent bound for the United States might enter via the Soviet embassy in Ottawa, Canada, then live in an intermediate country before moving to the target country to avoid detection.