Short answers, pulled from the story.
The United States boycotted the 1980 Summer Olympics in Moscow to protest the Soviet invasion of Afghanistan in December 1979. President Jimmy Carter announced in January 1980 that the U.S. would not participate unless Soviet forces withdrew from Afghanistan. The decision was discussed at a NATO meeting as early as the 20th of December 1979.
More than 60 countries joined the boycott to varying degrees. Sixty-eight National Olympic Committees that were invited did not participate, along with Qatar. Some nations boycotted entirely, while others allowed athletes to compete under the Olympic flag rather than their national flags.
Athletes had access to several alternative competitions, including the Liberty Bell Classic for track and field and the USGF International Invitational for gymnastics, both held in Philadelphia that year. These events could not match the prestige of the actual Olympics.
Muhammad Ali traveled to Tanzania, Nigeria, and Senegal at the request of the Carter administration to advocate for the boycott. He did not succeed in convincing Tanzania, Nigeria, or Senegal, but he did successfully persuade the Kenyan government to join the boycott.
The Soviet Union and its satellite states boycotted the 1984 Summer Olympics in Los Angeles in retaliation for the 1980 boycott. The 1980 boycott also influenced closing ceremony protocol: rather than raise the American flag in Moscow, the Los Angeles city flag was used instead, after IOC Director Monique Berlioux found a difference between the French and English versions of the rulebook.
Yes. In April 1981, a Federal District court in Manhattan approved the settlement of two lawsuits filed by more than 9,000 Americans seeking refunds. Americans who canceled before the 1st of March 1980 received 85 percent of their costs back; those who canceled after that date received 63 percent.