Danish and Norwegian are dialects, Swedish qualify as a separate language. "Nynorsk" ("New Norwegian") is a new language designed specifically to qualify as a new language, mainly for political reason (Norway was a colony of Denmark).
That all depends on your definition of "language". For most linguists, all that matters is mutual intelligibility. For others, a language is a "dialect with an army and a flag", i.e. a political construct.
A Swedish person like me most of the time have no trouble at all understanding spoken Norwegian, and reading both bokmål and nynorsk is quite easy. Spoken Danish requires some effort and getting used to, but it is still quite possible to have a conversation.
