1. Reauthorize iTunes - If that doesn't work, contact iTunes because something is screwy with your account. For future reference, I'd take the view that a password like that, linked to your credit/debit card is none of their business, and you'd be better backing up _everything_, deauthorizing and completely wiping and reinstalling OSX before sending it in.
2. I think that the best way to get round this is by disabling auto syncing, and just dragging songs across to the iPod on both computers.
David.