Having decent relations with the Pope is always a good thing, but you usually don't have to do anything special to maintain it. He's usually happy enough.
Marriage-wise, I try to expand my borders by marrying nearby female heirs to duchies and counties. There's not much near Iceland, besides maybe the duchy that comprises the Ornkey islands and other minor islands north of Scotland. Failing that, make sure you marry someone who nets you a good alliance or good traits that will be useful (i.e. a good Stewardship score to boost your tax income and economic tech development). You get prestige if you marry up (i.e. a princess of a king or emperor) and lose it if you marry down (i.e. a courtier or a countess) too.
Claims are always handled on an individual basis--i.e. your character. I don't know if you start with any claims, but it will be on a line in the character screen below your current titles if you do. If you don't have any, you can fabricate some with a good chancellor (high diplo score)--do it within your kingdom and your king will not interfere when you invade to take that territory. Make sure the crown authority stays low, though, because above limited crown authority the King forbids his vassals to fight each other.
