How Nilfgaard Wins the War?

Thanks to the assassination of King Radovid, Nilfgaard wins the war. Fearing guerrilla attacks, Emhyr made a deal and restored the country of Temeria. More information on how to get this ending in the Best Outcome of the War.

Can Nilfgaard win the war and Ciri become a Witcher?

tldr: Yes. The only requirement for the Ciri Witcher ending is not to visit Emhyr after the Kaer Morhen battle. After that, assuming she lives, she becomes a Witcher.

How is Nilfgaard powerful?

It has expanded mostly through the conquest of foreign countries, which were then turned into provinces of the Empire. The Empire's inhabitants believe that "real" Nilfgaardians are only those born in the heart of the Empire, and not those born in the conquered provinces.