How to tell if an iPhone is hacked and how to prevent it?
I don't really know why people always think their device is being hacked after something weird is happening in their eyes.

If she made a backup on a computer, and someone put that version back - they have access to the complete iPhone after restoring it on another device. Can this be the case?

If not, he said things during fights on iMessage? Maybe he just said it and regret it afterwards claiming he didn't send it. I don't see why anyone would add extra text to a fight and not use it for something else (if they really have bad intentions.)

Backing up an iPhone to a Mac does not turn on iMessage by default unless the user activates this him/herself. It is impossible to get active just because of a backup.

Solution
Change the Apple ID password and all default Apple services will become useless because it will prompt for the new password.