It considers "ramyun" to be incorrect. I would expect that to be an acceptable way to write 라면.
Usually its ramyeon but it seems like a lot of courses and books just translate it to ramen, maybe because more people are familiar?
Theyre definitely similar, but not the same
English doesn't have many words borrowed from Korean. Most Korean restaurants here have it as ramen on the menu, along with tofu and udon.
The Japanese got to us first, so that's where the language will take its word from.
Actually, the Chinese got to us first with lomein. But those are prepared without broth so the connection is not often made.