What mountains run north to south Russia?
The Ural Mountains.
The Ural Mountains that run north-to-south in Russia, are the primary landform that divides Europe from Asia. Farther south, the Caucasus Mountains run west-to-east between the Black Sea and the Caspian Sea. Although Georgia and Armenia (south of these mountains) are often considered part of Eastern Europe, Anatolia in Turkey is considered western Asia.
What are the chain of mountains that run nearly the whole length of the south island of new zealand?
No. West of the Sierra Nevada mountains, rivers generally run west, and east of the Appalachian mountains, rivers generally run east. Between those mountain ranges, most rivers run southeast or southwest, mostly draining (eventually) through the Mississippi River. (The Rio Grande is the only major exception I can think of. )