Finnish is in its own language family altogether, and I don't even know if it's any more closely related to Scandinavian languages than anything else. For all I know it might be a distant cousin of the Slavic languages, or perhaps you'd have to goi all the way back to some Proto-Indo-European language to find a link with other European languages.
Finnish is a part of the Fenno-Ugric language family. The other members include Estonian and Hungarian, plus a number of smaller languages. Estonian is somewhat possible for a Finnish-speaker to understand and vice versa. Hungarian is completely different though. It's funny when someone's speaking Hungarian in TV for example, and I'm not paying attention, I could mistake it for Finnish, but when I do pay attention, the words make zero sense to me.
But my understanding was that Iceland was settled by Scandinavians - not sure which. The Danes, maybe?
The first inhabitants of Iceland were Irish monks. Then settlers from Norway moved in, and they decided to pack up and leave, IIRC.