Short answers, pulled from the story.
Alexei Leonov performed the first spacewalk on the 18th of March 1965, during the Voskhod 2 mission. He was outside the spacecraft for 12 minutes and 9 seconds, connected to the capsule by a 4.8-metre tether.
Leonov's spacesuit inflated in the vacuum of space to the point where he could not fit back through the airlock. He had to manually open a valve to bleed off the suit's pressure before he was barely able to re-enter the capsule.
In July 1975, Leonov commanded Soyuz 19 in the Apollo-Soyuz Test Project, the first joint space mission between the Soviet Union and the United States. The two capsules docked in orbit and remained linked for two days, with American commander Thomas P. Stafford leading the Apollo side.
Clarke dedicated 2010: Odyssey Two to Leonov and Andrei Sakharov after the two men formed a connection at a 1968 screening of 2001: A Space Odyssey. Leonov pointed out to Clarke that the film's opening celestial alignment closely matched his own 1967 painting Near the Moon. Clarke named the fictional spaceship in the novel the Cosmonaut Alexei Leonov.
During his 1965 Voskhod 2 mission, Leonov drew a small sketch of an orbital sunrise, the first work of art made in outer space. On the 1975 Apollo-Soyuz mission, he brought coloured pencils and paper and drew portraits of the American Apollo astronauts who flew with him.
Leonov was twice named Hero of the Soviet Union, first on the 23rd of March 1965 for the Voskhod 2 spacewalk and again on the 22nd of July 1975 for the Apollo-Soyuz mission. He also received the Fédération Aéronautique Internationale Gold Space Medal in 1976 and the USSR State Prize in 1981.