Are my Skype communications private

The content of Skype communications is encrypted, though Skype and eBay which owns Skype have the capability to decrypt traffic. The risk of your conversation being intercepted and decrypted is very low, but it would be relatively easy for someone to determine that you are having a conversation, and what the IP addresses are for the interlocutors. Depending on how your network and Internet access are configured, your IP address may or may not be capable of being traced to you personally, or your home address.