Are part of Denmark, not the UK. The other ones you mentioned are essentially part of the UK (I'm too lazy right now to look up the official terminology in the UK is for them).
I’ll let you deal with the threats from Faroese that you dare not respect their autonomy and/or independence, but — Yes, you are right: I picked the wrong crown that they are not controlled by.
I can’t remember: they are not part of the EEA, somehow, right?
Guernsey, Jersey, Man and Gibraltar (how could I forget the already overlooked victim of Brexit) are “Crown dependencies,” i.e., like dozens of countries, King Charles III is nominally the sovereign, but it’s somewhat closer. The main difference with say Jamaica or New Zealand is that were attached to the EU, and their passport is de facto a British passport (and used to be de facto an EU passport), but it didn’t say so on the booklet itself. They just had exceptions in the fine print of each international treaty. All have exceptions carved for the weirdest thing, like who is allowed duty-free alcohol on boats to and from…
Are part of Denmark, not the UK. The other ones you mentioned are essentially part of the UK (I'm too lazy right now to look up the official terminology in the UK is for them).