This hotel does not have a shuttle.
No - there is no airport shuttle from the hotel. We took a taxi which was really expensive so be sure to agree the price with the driver! Uber could be an alternative! There is also a Train (slow) from the airport but we did not check that out!
I don't know if they have a shuttle, but it is very easy to take the train to within a few blocks.
Don't know. Drove there and parked across the street for $9 per day
Not sure because we took Uber to the hotel.
Get an answer from The Blackstone, Autograph Collection staff and past guests.