Is it possible to hack facetime and text messages from a iphone you do not own. We have the same apple id log in for both facetime and itunes. There are records of facetime calls, text messages and emails on one of our iphone which we did not make. How is this possible and what can be done to stop it?
The history of your calls and messages will be stored in your device but in an encrypted manner which even apple doesn't share or record them in iCloud. So FaceTime and iMessage are safe. But if you give your Apple ID and password to someone else, than can have a hand over the messages. So you can protect them by enabling Two step Verification for your device and by Creating App-Specific Passwords.
Everything about Two step verification https://support.apple.com/en-in/HT204152
Everything about App-Specific Passwords https://support.apple.com/en-in/HT204152