Actually in this context i agree with Go korea. 'good luck' doesn't make any sense here. In fact i don't think 'good luck' is a good translation for 'fighting'. The feeling is different. I played a lot of sports tournaments in Korea and the feeling is different from 'good luck' in a lot of contexts. 'do your best' would be better
파이팅/화이팅 has many translations depending on the context. It can mean "go" like "go Korea", it can mean "you can do it" before you do something difficult like a test, or it can mean "cheer up" after you bomb said test. I generally just think of it as "keep your fighting spirit high" and don't worry about it too much after living here in Korea for 3 years, it just means a Korean is trying to be nice to you.
It's not really borrowed as it doesn't have the same meaning, didn't come from having had it, and even violates the grammaticality of the word if it were borrowed directly. It's Konglish like 핸드폰. I'm also not sure I get the point you want to make. It's a commonly used word in Korean like many of the others in this course.