The shuttle from the airport to the hotel is free; they ask that you call them once you have your bags. It took about 15 minutes before they picked us up. The cost from the hotel to the cruise terminal is $12 per person & $10 per person back to the airport.
The parking was a part of the hotel package so check your confirmation or call the hotel direct; they did not charge additionally once we arrived. Yes, the car does stay on property in a designated area however it is not gated. I believe theire is a small each way shuttle charge. The hotel is close to the port. I hope you have a great cruise.
This hotel is within walking distance for restaurants and shopping. The shopping is a little further away. There is an excellent Cuban restaurant across the road leading to the two hotels here that are side by side. If you're going somewhere other than this restaurant I would recommend taking a cab. Safety would be my first concern and there are some areas that aren't so nice just a few blocks away.