Is FaceTime free (including internationally)?
Both FaceTime and FaceTime Audio are data and never go through the phone network as a regular phone call. You will be charged in the same way as using the internet for other purposes on your phone, over Wi-Fi or mobile data depending on your scenario.

FaceTime Audio calls don't ‘become’ regular calls. I'm almost certain the case from the linked article must be describing user error, calling someone not through FaceTime Audio but a normal phone call, and the user mistook the buttons they were pressing on their phone.

Besides any network fees, Apple does not charge a toll or fee to make or receive any calls. The license to the software and iCloud infrastructure is included with the cost of the Apple hardware.

There are certain countries that prohibit FaceTime services such as Saudi Arabia and UAE so you would not be able to make FaceTime or FaceTime Audio calls to these locations, but this would not cause a switch to normal calls. Net neutrality is evolving in several countries and there is no technical reason why FaceTime audio or video couldn’t be charged for above and beyond other forms of data.