is there jfk airport shuttle available

YES FAIRFIELD INN PROVIDE JFK Shuttle Provide you have to booked at the Reception

Yes

There's a shuttle TO JFK every 30 min starting at 4 AM, but the shuttle FROM JFK will pick you up from the nearest subway stop and you need to call the hotel to request ot once you are there.

Yes. Every 30 minutes.

Be sure to reserve your spot when you check in...

Yes it does