Is there a specific term for sea in Korean?
No, they're interchangeable, but 바다 is pure Korean, while 해 and 양 are Chinese characters. 양 as in Pacific Ocean, 태평양.
북극해 is Arctic Ocean.
What about 푸른?
Sea isn't accepted?
It is now (2019-02-13).
2019 -8: this lesson listens to you.