Libertarian has different meanings: https://en.m.wikipedia.org/wiki/Libertarian_socialism

Yes, but since Iceland is geographically part of Europe, it is better to use the European definitions to avoid ambiguity.

I'm not sure what you're referring to; I live in Europe, and the Center of Libertarian Culture near my house is socialist. And if you read the link, it explains that the term originated in Europe and meant left-wing anarchist. I think right-wing libertarianism is mostly an US thing.

Half the libertarian position is typically about being very socially liberal (privacy, freedom of speech, religious freedom, marriage equality (via removal of the state from that equation), drug decriminalization/legalization, et al). The pirate party tends toward socially liberal based on what I've read over the years. Correct me if I'm wrong.

They originated from Sweden's Pirate Party, which to a large part is social liberal (a mix of socialist and advocating individual freedom). While not all "copies" of the party abroad necessarily has adopted the same position, it seems many of them did.