Facetime "call failed" error on iMac

My mother’s Facetime on her iMac has started acting strangely. (It is working fine on her iPad and iPhone) Actually, there are two issues with the iMac, which i suspect might be related.

Any Facetime calls initiated from the Mac are met with a “call failed” error. (They can be made and received on the iPad and iPhone.)

We’ve also noticed that when she signs in to the iCloud website on her iMac with her Apple ID, the password is initially rejected. However, when selecting “sign in with another account” the same credentials are accepted.

Any ideas about what might be going on?

We’ve tried deleting Facetime preferences and the saved AppleID files in Keychain access, and reinstalling Catalina but the problem persists. We’ve also checked the date and time settings to make sure they are set to Automatic.

This seems to have started a couple of weeks ago after she was prompted by Facetime to sign in to her AppleID. When she did so, she noticed the call history that was displayed did not look like her most recent call history, with some unknown calls showing, possibly spam. She deleted the call history log at the time. We've also changed the AppleID password.

Any suggestions much appreciated.

She is using a 2015 21.5” iMac running Catalina.