Short answers, pulled from the story.
Mitrofan Belyayev was a Russian timber merchant and amateur viola player who became a music philanthropist and publisher after hearing the First Symphony of the sixteen-year-old Alexander Glazunov. He founded a music publishing firm in Leipzig in 1885 and established the Russian Symphony Concerts, a series open exclusively to Russian composers.
Members of the Belyayev circle included Nikolai Rimsky-Korsakov, Alexander Glazunov, Anatoly Lyadov, Vladimir Stasov, Alexander Ossovsky, Witold Maliszewski, Nikolai Tcherepnin, Nikolay Sokolov, and Alexander Winkler, among others. The circle met in Saint Petersburg between 1885 and 1908.
Both groups believed in a uniquely Russian style of classical music drawing on folk and exotic elements, but the Belyayev circle, unlike The Five, accepted the necessity of rigorous Western academic training in composition. The Belyayev composers also tended to imitate existing Russian styles rather than actively seeking out new folk material as Balakirev had done.
The premiere of Rachmaninoff's First Symphony on the 28th of March 1897 was a disaster. Rimsky-Korsakov had told Rachmaninoff he found the music disagreeable, and critic César Cui published a review likening it to what a student at a conservatory in Hell might compose. The symphony was not performed again during Rachmaninoff's lifetime, and he suffered a three-year creative collapse.
Belyayev established an annual Glinka prize in 1884, named after pioneer Russian composer Mikhail Glinka, who lived from 1804 to 1857. It was one of several patronage mechanisms Belyayev created to support Russian composers.
After Rimsky-Korsakov's retirement in 1906, his son-in-law Maximilian Steinberg continued the circle's aesthetic at the Saint Petersburg Conservatory through the 1920s. Other conservatories across Russia, including those run by Ippolitov-Ivanov in Moscow and Reinhold Glière in Kiev, also retained strong ties to the Belyayev aesthetic well into the Soviet period.