No, Rockefeller Center is in Midtown, between 6th Avenue and 5th Avenue, from West 47th to West 50th Street.
The Financial District of Lower Manhattan.
The Battery is the part of lower Manhattan where the World Trade Center site was located.
Lower Manhattan has no official definition but generally refers to the area below 14th Street, although there are references to "lower Manhattan" as being below Canal Street or below 23rd Street.
The Rockefeller Center was declared a National Historic Landmark in 1987 and is partially known just for its vast size, consisting of 19 commercial buildings that span 22 acres of land. Part of what makes Rockefeller so special is that the buildings within the center are historic buildings that date back to the early to mid 1900s.
None of it. Construction did not start until 1929.
I think you must be talking about Manhattan, Kansas. However, there is no city in New York named Manhattan. Rather, Manhattan is one of the five boroughs of New York City: Manhattan, Brooklyn, Queens, The Bronx and Staten Island. Manhattan is the main borough (where Times Square, Wall Street, Harlem, Broadway, Rockefeller Center, Central Park, etc. are), so many people say "New York City" when they really mean, "the borough of Manhattan." However, technically Manhattan is not a city; it's just part of one.
What is now SoHo, TriBeCa and the lower part of the South Village.
The streets of New York City are arranged on a grid pattern, except for Lower Manhattan. Lower Manhattan is the oldest part of New York City, and its streets were formed long before the urbanization of the remainder of Manhattan.
The 10002 zip code encompasses the Lower East Side of Manhattan, and part of Chinatown.
The purpose of Rockefeller Center is commercial. The entire 22 acre complex is used by many businesses including Bank of America, Simon & Schuster, McGraw-Hill, and Time-Life. Radio City Music Hall is also part of the 19 building complex.
Wall Street is located in the Financial District of Lower Manhattan in New York City. It is a famous street known for being the historic home of the New York Stock Exchange and other financial institutions.
This ZIP code apparently belongs to part of Rockefeller Center in Manhattan. According to http://maps.huge.info/zip.htm it is bounded by 5th Avenue and 7th Avenue, and 50th Street and 48th Street, except for half of the block between 49th & 50th from Avenue of the Americas eastward to midblock (in other words, the GE Building).