When did Enrico Fermi invent the first nuclear reactor?

Answer 1

Actually Leo Szilard invented both the nuclear reactor and atomic bomb in 1933, applied for a patent covering both in 1934 and was granted that patent (GB630726) in 1936. The British Admiralty (Navy) immediately classified his patent to protect it from the Nazis (and kept it classified until 1949). Szilard however never attempted to build either at the time because no fissionable material was known until it was discovered by a team working in Germany and Sweden discovered that uranium-235 could fission.

Szilard contributed to starting the Manhattan Project by writing the so called "Einstein Letter" the warned FDR that the Nazis might be working on an atomic bomb. (Though called the "Einstein Letter" the only things Einstein did was read the unsigned letter shown him by Szilard, approve what it said, and sign it. Szilard felt it would have more influence on FDR if signed by a much more well known scientist than himself.)

Enrico Fermi only built the nuclear reactor, he did not invent it. Fermi's first nuclear reactor (CP-1 for Chicago Pile #1) first operated on December 2, 1942 (less than a year after the Japanese attack on Pearl Harbor). Fermi almost certainly had access to Szilard's (then classified) patent, but how much he depended on is is unknown.

Note: following the discovery of nuclear fission using uranium-235 in 1939, several people independently and almost simultaneously reinvented the nuclear reactor and/or atomic bomb without any knowledge of Szilard's prior art covered by his patent. At that point it was rather obvious to anyone that understood physics what was required.