Beware, you protected your email-address but it's visible in your second post, so I would edit that
Not sure it really matters, but you say you want to send your news via 3G, but the email@example.com
would transmit only via WiFi if I understood correctly.
I'm not sure the free.kindle.com even exists anymore, with the recent change in personal documents I think this was dropped, and there's only the @free.com address left. Someone will hopefully correct me on this if I'm wrong.
Another cause of the problem could be : in the error log, it seems you use a gmail account, are you sure your login / password is correct ?
Check the preferences in Calibre, where you set you email address you want to send to, you can test it there.