I like the idea of addons for country badges, but I would prefer to keep them as the same addons used for the main badge set. Also, badges for per cache type would clutter the country badge - I think it would be too much.
My preference for a country badge is exactly what there is now - the new style badges with flag, and possibly what addons as currently exist (although I would be fine without that). Would be nice to have the ribbon with country name, however some country names are too long and this may not be practical.
No to detailed statistics. This is an awards page, not a stats page.