Is it weird if your best friend in the whole wide world lives far away so you IM Skype her every night?

there;s nothing weird about your bff being your cousin, even with the age difference, but you should probably limit your skyping with your bff to 3x a week and use the other time to make new friends. For your long term happiness this is the best plan. You can make new friends and keep the old. My mom and her BFF have lived in different states for 30 years, but still talk all the time and visit each other every 2 months or so. However, they both also have friends in their own states. You can have several "best friends" from different parts of your life. And you should, it is best.