Questions about example sentences with, and the definition and usage of "Pyongyang"

A: It’s grammatically correct, but in normal speech “Korea” means the South.

A: You need to specify that Pyongyang is the capital of North Korea (rather than just Korea). The capital of South Korea is Seoul. So with the second sentence, you’re insinuating that if the Korea peninsula were to be unified as one country, you think that the North Korean capital of Pyongyang would become the capital city for all of unified Korea. I would suggest specifying that as well, since that is currently not the case.