A. Many NK models have real rigidities like efficiency wages. There remain NK models with nominal rigidities. Both kinds of rigidities make it possible for markets to fail to clear, but nominal rigidities respond quite differently to policy.
Most explanations apply isomorphically to both price and wage rigidities.
E.g. the Mankiw menu costs model. Hall lifetime employment critique of apparent nominal wage rigidity applies much less forcefully to prices. ADP psychological view applies much more clearly to wages than to prices. A sufficiently big shock will have no real effect. In general, problem can only last until next adjustment period.