Anguilla is a British Independent Island. They use Eastern Caribbean (EC) which is listed in all the grocery store prices. But everyone on the island accepts US dollars. Most places do accept credit cards with no foreign transaction fees. And to note they have a high hospitality tax in the restaurants. It is easier to pay in cash at a lot of places and there isn't really an easy way to get cash once on the island so just come with cash prepared and then there is a safe in your room so you don't have to carry it all around.
No you do not have to make your cell phone international. Most every where will have Wifi and you can login into Wifi and for making phone calls and text messages we suggest using Whats App so you don't have any additional charges.
You can do car rentals through Shoal Bay Villas the hotel. You will have to purchase a $25 drivers license. Please let me know ahead of time if you would like to rent a car and what days. Fun Fact: They drive on the wrong side of the road because it is a British Island.
Be sure to bring your own shampoos and toiletries. You can purchase at grocery store but more expensive. Bring CASH - you will need it to get on the off the island / some bars and restaurants it is easier to use cash. Be sure to call your card companies and let them know of your travel plans. You do not need to bring beach towels they are provided at the hotel for you.