first, for the shipping to be applied to an item, the weight must be set. if you leave the weight empty, it will be set to 0 and cause the shipping for that product to fail
If you have a shipping/Handling charge in the product additional settings, that will be applied in addition to whatever shipping rules you configure.
if you do not set a rule for a country, the customer will be alerted that shipping is not available and they should call. the number is set on the contact us page. that pages uses the store settings in the admin panel.