Whenever you are an AU on someone else's CC, both you and that person will share the same payment history, balances, CLs, stati, etc. It's no different in your case. If one defaults, then the other will show the same on their report.
If you are listed as an AU on a bad account, or even a good account, you can dispute as "not mine". He can't do that because the card is his, but you can do that because the card is not yours. And he can do the same to his account that he's listed as an AU on. The CRAs will remove the AU account.
For the unpaid CC CO, I recommend sending a PFD letter, or pay it off and send GW letters later.
For the CO that was paid in 2009, does it report a balance at $0? It can still report as a charge-off even after paid.
BTW, Welcome to the forums!
I'd suggest reading the following:
Credit Scoring 101 - great for knowing what is in your credit score and to see how your score is impacted.
What Steps Do I Take - great for learning the repair process.
and Example letters - PFDs, GWs, DVs, etc.
For the citi card debt it doesn't show a $0 , it shows the balance of $1,000.00 , which my Husband paid.
It should be reporting $0. I'd send a GW to them asking them not to update to $0, but to delete.