Some of these are of course dependent on which name you use. Czech Republic is officially Czechia, is it not? Cote d'Ivoire should be included, IMO. UK should not, as the name contains the words "Great", "Britain", "and" and "Ireland" - just as you quite rightly excluded St Vincent or St Kitts, for example.
As you said, most of these are subjective and depend on the names you choose to use, that's why I stated I'd be using the names shown in the "Countries of the world" quiz - where the names used for Czechia and the UK are "Czech Republic" and "United Kingdom" respectively :)