Make sure you phone ahead so they don't give your room away, happened to my coworker earlier this year when his flight was delayed, they ended up putting him up at a nearby hotel.

Free. But it's closed in the winter

I believe if you arrange it with concierge services they can help u

Newark is $90 and 40min to 1h30+ away depending on traffic if you have loads of luggage. JFK with airtrain+train+ subway is the way to go if you travel light.

I think it was the directive of the hotel, you may ask in the front desk and they will say who exactly did it, apparently it was laid out to apply to comfort to any type of guest