Uhura's bi-lingual ability was established in the first episode, "The Man Trap", when she spoke both Swahili and English. We learn in "The Changeling" that she has an aptitude for mathematics. And, in the sixth movie, that she was chairing a seminar at the Academy, thus implying that she was a highly-respected individual by other communication officers.
As for her age, we learn in ST III that she is a "...twenty-year space..." veteran. She is first seen in 2266 as a lieutenant on the Enterprise
. It's conceivable that she graduated the Academy in 2265, completed a tour of duty, and was assigned to the Enterprise
There is confusion on the age of Captain Pike. In the "Menagerie", he is described as having roughly the same age as Captain Kirk.