Is it possible to use public transport between NYC and red Hook? How long would it take to get there?
How to get from La Guardia to Red Hook, NY state
or from JFK to Red Hook
How to get from LaGuardia airport to Red Hook, NY
or how to get from JFK to Red Hook
#5 & 6 - From either NYC airport you'd have to get yourself into Manhattan (via cab or public transit) to Penn Station and then take the Amtrak train as mentioned in #3 above