Manhattan is a borough of the City of New York. The island of Manhattan is what most people think of when they think "New York City" and features sites like the Empire State Building, Rockefeller Center, Times Square, and Wall Street.
The other four boroughs are:
The Bronx
Queens
Brooklyn
Staten Island
There are many train stations in New York.
One can easily find a train station in New York by looking on a train station map. Train station and subway maps are posted in almost every gas station in New York. To view a train station map on the go, one can visit the official site of subway transportation and it will have listings of times and departure location.
Barney Millers' 12th precinct station was set in Greenwich Village, New York City
New York Penn Station
Yes. Metro North Hudson Line or Amtrak.
The best way to commute from Manasquan, NJ, to Manhattan is typically by taking a train. You can catch a New Jersey Transit train from Manasquan Station to either Long Branch or South Amboy, then transfer to a North Jersey Coast Line train to Penn Station in Manhattan. Alternatively, you could drive to a nearby station with direct train service to Manhattan or consider using a rideshare service, though traffic can be heavy.
Hudson, NY
JFK airport is in New York City, in the borough of Queens. Assuming you meant to ask about trains to the borough of Manhattan, you can take the AirTrain shuttle (for $5) to the Howard Beach Station of the A train (of the A-C-E, the blue line), and take the A into Manhattan.
12.50 one way.
Yes, Manhattan is in New York.
New York, New York is actually Manhattan itself. It's generally called Manhattan to distinguish itself from the state of New York.
There are four trains a day each way between New York Penn Station and Syracuse.