It depends on your privacy settings. If you have your privacy set to Public or Friends of Friends then people who are not your friends on Facebook can see your stuff. There is a little gear looking icon in the top right corner of Facebook, if you click on that you can change your settings and make your stuff only available to Friends.
It is possible for someone on Skype and is not your Facebook friend to see your Facebook details. This is on condition that you have not set your account as private. However, if you do not want them to view, you should go to settings then security and adjust your information.