Usually, best rates are at the banks and the worst rates at the hotels. Your very best rate will be when you use your credit card for purchases. Standard 110 volt. Many internet cafes have sprung up on Cozumel island. Access to email and the internet is easy and inexpensive.
Public telephones are abundant around town.
The Calling Station in town offers call to anywhere in the US for a small fee and might be your most economical option. Beware of credit card or collect calls made from public phones. You may come home to find a hefty surprise on your next statement. Just like anywhere else that's tropical, the sun is very hot in Cozumel and sunscreen is recommended, especially for children. You can purchase sunscreen and sun tanning products in Cozumel.