The Kansas City Science Fiction and Fantasy Society, the J. Wayne and Elsie M. Gunn Center for the Study of Science Fiction, University of Kansas and the Science Fiction Museum. (The Kansas folks founded the award and administer it, but the Hall of Fame is now located in the Science Fiction Museum in Seattle.)
Unclear, probably a jury.
You have to be very famous. You do not have to be dead. Four new members are inducted each year: two living and two posthumous.
Hall of Fame Inductee
Everlasting glory and a place in the Hall of Fame exhibit.
None. If the jury doesn’t know your name then you are, by definition, not eligible.