It is actually related!
There are two Proto-Germanic words; *kwēniz, a wife, which is responsible for the English word 'queen', via Old English 'cwēn', a wife of nobility.
The other word is Proto-Germanic *kwenǭ, a woman in general, which is responsible for the Norwegian 'kvinne', but also English 'quean', via Old English 'cwene', a licentious woman.
Not exclusively. German has five distinct ways of plural formation, -er among them. While Norwegian is much more homogenous in the formation of the indefinite plural, there are exceptions to the "just add -er" rule, for example ku - kyr (cow - cows), mus - mus (mouse - mice), tiger - tigre (tiger - tigers), datter - døtre (daughter - daughters), bok - bøker (book - books).