Torshavn does not belong in this list. NOt in the official world capitals list on Earth. Near misses: Riga, Tallinn, Vilnius, Vatican City, Rome, Stockholm, Helsinki and Reykjavik.
Yes it does: see the List of National Capitals. I guess your opinion depends on whether you think that the Country of Denmark is a country, or the Kingdom of Denmark is a country. We treat the Country as a country, and the Kingdom therefore as a supra-national entity, the members of which are the countries of Country of Denmark, Faroe Islands and Greenland.