Per the title, "Take Me Out to the Ball Game" is an early-20th century Tin Pan Alley song which is traditionally sung during the seventh-inning stretch of a baseball game.
As demonstrated by his throwing, Ross is a 'southpaw', i.e. a left-handed pitcher.
Natalie confuses Russ Nixon with Richard Nixon. The former was a catcher for the Boston Red Sox when this episode originally aired; the latter was, at the time, former Vice President of the United States and, in 1969, inaugurated for his first term as President, an office from which he resigned in disgrace 9 August 1974.