Speedlever is correct. If you have a wifi-only K3, it doesn't matter which address you use. Delivery via wifi is always free.
If you have a 3G+wifi model and don't want to ever be charged, there a two ways to do it. Either use the
xxx@free.kindle.com, or use the regular
xxx@kindle.com and set your maximum individual charge to $0.00 in your amazon profile.
3G-only K2's and DX's must use the
xxx@free.kindle.com to avoid charges.
As to the OP's problems; many times, Amazon servers see direct connection attempts from individual mail clients (in this case calibre on your PC) as spam related and drop the connection. They like to see connections from other smtp servers. Either configure your ISP's smtp server in calibre (or set up your own smtp server) or use gmail or hotmail addresses. And like Paul said, make sure your email address is added to the list of permitted email addresses in your Amazon account.