I don’t think it would be appropriate for a moderator admin to disclose confidential information to settle a dispute involving no money and only the disclosure of something that makes another forum user look bad.
It would be very much in forum's best interest to investigate an account hack and ban the perp if possible.
It would be unusual and counterproductive to ban someone hacking accounts. This would only force the person to connect to the forum via alternate means, and it would be difficult to know if it is the same person if he hacks more accounts. It would also make it more difficult to track possible vulnerabilities that need to be closed. It would be better to give the person rope to bang himself with and go to law enforcement with evidence of his crimes if he is causing a problem.
No, only admins.
And some
mysterious newbies 
I don’t think it would be appropriate for a moderator admin to disclose confidential information to settle a dispute involving no money and only the disclosure of something that makes another forum user look bad.
Admin doesn't have to disclose information (like IP addresses), but could share the result of such an investigation (
like in JusticeForYou's case).
In that case, the person submitted to the disclosure of information. BitcoinGirl.Club can show anyone his IP logs, which can be accessed by any user. This is also different as in this case, someone is recovering their account while in the J4Y case, he was trying to prove he was the original owner.