Nah, this part:

> Usernames must be unique and can only be registered by one commenter at a time. If you are seeing this message, it means your desired username is already taken, and you should try registering a different name.

The journalist didn't just google that username and assume everything he read was from her or something, he simply clicked on her linked account in the Disqus system and read/screenshot what else she posted. She's obviously lying when she said that the racist comments, but only the racist ones were written by someone else.

Not clear. Suppose she has a spouse, roommate, son, friend, etc who uses the same computer and since her account is automatically logged in, comments from the same account.

If she could bring someone who would say "Yes, I wrote that on her account" or show that the time of the comment she was teaching or something - I think that would be pretty compelling.

I think they were referring to the guest commenting option.

https://help.disqus.com/en/articles/1717211-guest-commenting