Short answers, pulled from the story.
The Reykjavík Summit took place at Höfði, a building that formerly served as both a French consulate and a British embassy. This structure stood on a hill overlooking the harbor of Reykjavík, Iceland.
U.S. President Ronald Reagan and Soviet General Secretary Mikhail Gorbachev met at the Reykjavík Summit on the 12th of October 1986. These two leaders engaged in intense negotiations regarding arms control and human rights during their meeting.
The Reykjavík Summit ended without an agreement because Ronald Reagan refused to compromise on Strategic Defense Initiative testing limits while Mikhail Gorbachev insisted on confining research to laboratories. Their disagreement over these specific conditions caused the talks to stall despite getting close to eliminating all nuclear weapons.
The Reykjavík Summit facilitated the INF Treaty signed at the Washington Summit on the 8th of December 1987 by laying groundwork for future disarmament agreements. Participants discovered the extent of concessions each side was willing to make, which proved crucial for subsequent negotiations leading to major treaties.
Ronald Reagan sought to include discussions on human rights, emigration of Soviet Jews and dissidents, and the Soviet invasion of Afghanistan. Mikhail Gorbachev focused strictly on arms control and proposed limiting talks solely to military reductions.