The correct answers are:
Buddhism
While this philosophical and spiritual doctrine originated in what today is India and Nepal, it spread largely through China around the 6th century AD. From China, it entered in Korea where it became the main religion and developed its own interpretation and variants.
Confucianism
Confucianism is a set of moral doctrines that emerged in China following the teachings of Kung-Fu-Tzu (Confucius) around the 6th century BCE. This philosophy shaped strongly the social and political life of China and other Eastern Asian peoples, like Korea.
Movable type
The Movable type is a printing technology, and the first known technology of this kind was invented in China in the 11th century AD by the Chinese inventor Bi Sheng. From China, this technology entered in Korea and during the 13th century the Koryo dynasty invented a metallic movable type.
Celadon pottery
Celadon is a kind of ceramic originally from China. Celadon pottery entered into Korea from China and it became very popular and an important cultural feature of this country. Korean celadon pottery was very extended mainly during the 10th and 11th centuries under the Goryeo dynasty, that produced the Goreyo pottery also known as classic Korean ceramic.