There is a small fee if you download over 3G. You can prevent that by setting the charge limit on your "Manage my Kindle" page to $0.

Wifi is always free. (source: http://www.amazon.com/gp/help/customer/display.html/ref=hp_l...)

The e-mail pops out on your desktop pc or whatever you use. You can then copy it to the kindle via usb or whatever you prefer.

Only over wifi.