"Meanwhile there is also the problem with cultural fight over who invented what."

I think this is a very silly fight.

"China is extremely unhappy with the THAAD in S. Korea."

The Skoreans only have themselves to blame. THAAD's radar can look deep into China and give very early and accurate warning to the murrikans. That could put a dent on China nuclear 2nd strike capability. There is a limit to what China can tolerate.