In terms of OP/Ed of an anime, it is more likely to find Opening and the Endings that is produced by Korean Artist (singing in Japanese)than featuring actual Korean songs.
In the 15th Opening of Fairy Tail, Masayume Chasing. It is sung by a Korean Singer goes by the name of BoA. Here is the link of the song in short ver
As for ...
Well in general anime is usually distributed through, including Japan,
Videogram (DVD, Blu-ray)
TV (Technically it's Broadcasting)
Screening on Theaters for Movies
Internet i.e Streaming
Now if you are asking whether NHK is the only corporation that broadcasts anime, then the answer is No. In many cases, the said anime series is broadcast only in the area ...