can you name any of her successful works during 1932 to 34?
"A Bill of Divorcement" and "Christopher Strong"
Katharine Hepburn
On the strength of "A Bill of Divorcement", RKO signed her to a long-term contract. George Cukor became a lifetime friend and colleague—he and Hepburn made ten films together.

Hepburn's second film was "Christopher Strong" (1933), the story of an aviator and her affair with a married man. 
was katharine hepburn an actress? Yes, an American actress. when did she start working in theatres? November 12, 1928 which theatre? Cort Theatre what was its record in box office? The Tony Award-winning revival of "Fences" achieved the box office record.
wiki:11602156
Katharine Hepburn [SEP] Hollywood success (1932–1934)
For playing aspiring actress Eva Lovelace—a role intended for Constance Bennett—in "Morning Glory", she won an Academy Award for Best Actress. She had seen the script on the desk of producer Pandro S. Berman and, convinced that she was born to play the part, insisted that the role be hers. Hepburn chose not to attend the awards ceremony—as she would not for the duration of her career—but was thrilled with the win. Her success continued with the role of Jo in the film "Little Women" (1933). The picture was a hit, one of the film industry's biggest successes to date, and Hepburn won the Best Actress prize at the Venice Film Festival.