Short answers, pulled from the story.
Russia has twenty-one internationally recognized republics, each created as a national homeland for an ethnic minority called the titular nationality. A twenty-second republic, Crimea, is under Russian control but is internationally recognized as part of Ukraine.
The modern republics were established with the Federation Treaty on the 31st of March 1992, which dissolved the Soviet-era Autonomous Soviet Socialist Republics. Their origins trace to Vladimir Lenin's Declaration of the Rights of the Peoples of Russia on the 15th of November 1917, which promised minorities the right to self-determination.
The republics of Russia have the right to establish their own official languages, maintain their own constitutions, and have national anthems, rights not granted to krais and oblasts. During the 1990s, bilateral treaties also gave some republics control over natural resources and foreign relations; Tatarstan and Bashkortostan were permitted to conduct their own foreign relations and sign agreements with foreign governments.
Putin's centralization reforms began with the creation of federal districts on the 18th of May 2000 and continued through the gradual expiry and termination of the bilateral power-sharing agreements negotiated in the 1990s. The last such agreement, held by Tatarstan, expired on the 24th of July 2017. After that point, some commentators concluded that Russia had ceased to function as a federation.
Chechnya was formally reintegrated as the Chechen Republic on the 24th of March 2003 following the Second Chechen War, but operates with broad autonomy under Ramzan Kadyrov, whom Putin appointed in 2007. The republic runs its own security forces, conducts its own de facto foreign policy, and receives generous federal subsidies; observers characterize it as a state within a state.
Stalin reversed the earlier policy of indigenization in the 1930s, making Russian mandatory across non-Russian areas and purging minority leaders from government. Between 1943 and 1945, ethnic Balkars, Chechens, Crimean Tatars, Ingush, and Kalmyks were deported en masse, and the Soviet government dissolved their republics. Khrushchev rehabilitated the deported peoples after Stalin's death on the 5th of March 1953, restoring most but not all of the dissolved republics.