Hi Gretch,
The brand new JFK JetBlue terminal is awesome.
Every gates are in the same building.
I never miss a connection with JetBlue so I cannot say if they will automatically put you on the next flight. But if you consider that you cannot put all the passengers of a flight into another unless both are at 50% full it might not be automatic...
Take a look at this JetBLue JFK link:
http://www.jetblue.com/about/jfk/