Dont know the answer to the visa question - have seen differerent answers at differerent times.

Stayed one night last week at this hotel. One of the really nice things they did was to send an email a few days before with the location of the shuttle and schedule from each terminal. This was really helpful given the size of the airport. We arrived on a domestic flight at Terminal 2, waited 20 minutes took the shuttle, checked in, went back to the airport and into town for the day, via airport and subway express - very easy and quick to do. Returned to the airport and shuttled back to the hotel in time for exec lounge snacks at dinner time, very good selection. Had flight at 8am, breakfast restaurant was open at 5:30am so had time to eat and catch the 6am shuttle to terminal 3. HH Diamond - upgraded to a mini-suite, very nice with a living room, and large bedroom. Fitness center and pool are also very nice.