Cpuff~I"ll try to answer a couple of your quesitons..
You "shouldn't" have a problem calling out of your room. Having said that we have already had a "temperamental" phone while staying at CSA. We bought a digcel phone there in Negril on one of our first trips so usually use that for both local and international calls.
Getting transportation is not problem,you can use the route taxi system if you just want to go someplace along the beach road,go out in front of CSA( we usually walk a bit so we're not right in front of it) and point to the road.. wont be long before a taxi stops.. (just make sure it has a red plate and the route written on the side) Lots of info on here about route taxis but if you need info I"ll be glad to explain how they work. When we go to the cliffs we usually negotiate a rate with one of the route drivers to take us there. I"m sure the front desk or one of the guards outside of CSA would also arrange it for you. Not sure of price.Also, a number of the more popular places like Ivans will you up for free, you just pay for ride back.
The shuttle.. it wasn't until I went to answer you on this that I realized we never took the shuttle to CSA. We stay on the cliffs for a few days before going to CSA so always arranged our own transpiration. We have taken the Couples shuttle to their resorts in Ocho Rios and it was fine. Never had to wait long for it to leave the airport and one time stopped on the way and the other time went straight to the resort. Its up to you whether you want to spend a little extra $ to skip the shuttle. Pros and cons both way.. We've always used Clives Transportaion , you can also arrange excursions with him. I know they have a tour desk at CSA but I"ve never used it so can't help there.
Feel free to pm me... like I said.. I"m already missing CSA and Negril and I"m going to have to live vicariously through others until next year.
Have a great trip!