Can't answer your first question but you will have to add international roaming and AT&T will charge for that. Not sure how much the cost will be as we turn our phones off except for WIFI when we get to the Island. Suggest you check with AT&T regarding the different options.
When you are in Jamaica, your cell phone will no longer get ATT service. It will get either Lime or Digicell. If you don't have a plan through Lime, Digicel, or perhaps ATT, you will charged $2.99 a minute for calls. There are several threads regarding phones on the board. Do a search to find them. When reading the other threads, you will see other alternatives.
I have ATT, works fine. Call ATT to turn on international roaming. No charge for that. If you do a voice call it cost $2 per minute and text messages cost $.50 per message both incoming and outgoing. You dial you voice call just the same as in the US (1- area code - number)