yes
No, Gene Autry is not Alan Autry's father but is a distant cousin. Alan's biological father is Carl Autry, whom Alan did not meet until 1982.
Gene Autry had no children, and Alan's bio makes no mention of any relationship to Gene. So any relationship is tenuous at best.
Alan Autry is 59 years old (birthdate: July 31, 1952).
In 1932 he married Ina May Spivey (who died in 1980) and In 1981 he married Jacqueline Ellam, who had been his banker