Currently, fixed per product rate always overrides the global shipping settings (user-defined and carrier-calculated). Therefore, if you have set “Free” or “Fixed” shipping freight on the product modify page, global shipping methods will not be applied to this product.
Unfortuntaely, Ecwid doesn’t allows to set shipping methods for each product separately. If you consider that this functionality should be added in Ecwid, please, vote for this idea here:
and we will email you when it is released.