all Korean schools teach Korean
Are you referring to the North or to the South Korea? For any Korea, depends on the Korean law related to school admission by foreign students. An easy way to check it out is to consult the Korean Embassy of your country.
Korea in Korean is "hanguk"
Around 70-80% of Korean high school graduates go on to attend college in Korea. This high percentage is due to the strong emphasis placed on higher education in Korean society.
No it is not. Korea has Korean people and most people there know only Korean (unless they are learning spanish or other languages at school) .
North Korea and South Korea lie on the Korean Peninsula.
You speak Korean in Korea.
The official language spoken in North Korea is Korean.
The nationality of Korea is Korean.
The nationality of Korea is Korean.
Two countries have Korean as their official language: North Korea South Korea
The primary country where Korean is spoken is South Korea. North Korea also speaks Korean. Additionally, Korean is spoken by minorities in China, Japan, and other countries with Korean diaspora communities.
Korean is the official language of only North Korea and South Korea. However, there are large minority groups that speak Korean in China, Japan, US, and Russia.