Short answers, pulled from the story.
Richard Rodgers and Oscar Hammerstein II first met at Columbia University in 1920. They collaborated on the Varsity Show titled Fly With Me where Rodgers wrote songs as a freshman while Hammerstein served on the judging committee.
Oklahoma! opened at the Shubert Theatre in New Haven on the 11th of March 1943 before moving to Broadway. The show ran for an unprecedented 2,212 performances until closing on the 29th of May 1948.
South Pacific addressed racism through the song You've Got to Be Carefully Taught supporting interracial marriage. Rodgers and Hammerstein refused to remove it from the show even if it meant failure when lawmakers proposed outlawing entertainment inspired by Moscow due to offense taken.
The original cast included Alfred Drake playing Curly and Joan Roberts playing Laurey. No stars were used in the production despite typical musicals being written around talents like Ethel Merman or Fred Astaire.
Cinderella aired on CBS on the 31st of March 1957 becoming their only collaborative effort written specifically for television. More than 107 million viewers watched the broadcast with Julie Andrews playing Cinderella.