Were all fairies exterminated? On episode 19 there are some flashbacks from King which imply that most of them got wiped out. However I'm still a bit unsure...

Is there a fairy realm? Are there any fairies still alive?
According to the wikia page, some of them are still alive and living in the forest that Ban planted from the seed he was entrusted with by Elaine. There is a fairy realm and it is linked to the human world by the Fairy King's Forest.


  Several year later, fairies begin to inhabit the newly restored Fairy King's Forest after Ban planted the Almoca Seed entrusted by Elaine.