Short answers, pulled from the story.
Mitrofan Belyayev established the organization in 1884 by creating an annual Glinka prize named after Mikhail Glinka. He later founded a publishing firm based in Leipzig, Germany two years after that event.
Nikolai Rimsky-Korsakov served as one of three advisory council members who reviewed compositions and determined patronage for aspiring musicians. He taught many members at the Saint Petersburg Conservatory before he retired in 1906.
Sergei Rachmaninoff stopped performing his First Symphony because Nikolai Rimsky-Korsakov criticized the work as disagreeable during a rehearsal on the 28th of March 1897. This rejection caused a psychological collapse leading to a three-year creative hiatus where he produced almost nothing.
Francis Maes writes that composers from the Belyayev circle are often described as important links to modernist Russian composers such as Igor Stravinsky and Sergei Prokofiev. However, this connection suggests modernism resulted from a radical break rather than a gradual process.
The circle set up an establishment that controlled the flow of new music across Russia well into the twentieth century. Maximilian Steinberg maintained this system through the 1920s and traditionalists like Ippolitov-Ivanov ran conservatories in Moscow and Kiev during the Soviet era.