In a city where more than 100 languages are spoken, many parents believe learning a foreign language can help their children learn their cultural heritage and give them an advantage in their academic and professional pursuits. An Italian-American mother is on a crusade to push the city to start an Italian dual-language program so her daughters can learn the language that her great-grandparents spoke. Although the number of Americans learning French has declined, the language remains sought after among the city’s Francophone families. A Hebrew charter school in Brooklyn is hoping to open a school in Harlem, which already has more than 20 charter schools. West to the city, Facebook is funding a public high school that opened door last year with the only Chinese-language program in Newark.