The interviewer is meant to be Louella Parsons, a popular gossip columnist at the time. Bugs even calls her by her nickname "Lolly".
"That's thirty for today" references an old expression meaning the end of a story. 19th century telegraph operators used "XXX" as an end-of-message flag to confirm that the message did not get cut off in the middle. Roman numerals XXX equal 30, so "30" came to be slang for the end of a story and, later on, the end of anything, including a speech, a work shift or even life.
The title is a play on "A Tree Grows in Brooklyn," a coming-of-age novel set in early twentieth century Brooklyn. Not only is the book used as a sight gag here, Bugs actually is seen reading it at the end of the short.
As befits his Hollywood celebrity status, Bugs keeps his carrots in a monogrammed gold cigarette case.
Familiar New York sights include a Stork Club parody, an automat eaterie, rooftop water towers, a skyscraper, and clotheslines strung between apartment buildings.