TSA staff is slow, unfriendly and not clever. Like service in collapsed USSR. They speak with passengers like with prisoners. This is a shame for America in common and for NYC in particular.
Don't bother with Airtrain TO this airport. MTA service changes are constant, ongoing, and impossible to decipher. You will miss your flight, I promise. However, Airtrain FROM JFK is fine.
John F. Kennedy International Airport is the primary international airport serving New York City. It is the busiest international air passenger gateway into North America, the 14th-busiest airport in the world, and the sixth-busiest airport in the United States.