"What kind of hamburger do you have?"
Translation:무슨 햄버거가 있습니까?
무슨 and 어떤 have a very small nuance. 무슨 means something like "I have no idea which ones there could be" - 무슨 음반이 있어? = what/which albums do you have? (could be anything)
어떤 means something like "of the few obvious choices, which one?" - 어떤 영화 볼까? = which movie should we see? (if you're at the movie theater, there are around 7 choices)
My understanding is 어떤 is a better word to use here. I'm not native and could be wrong.
why does this translate to "what kind of hamburger do YOU have"? it doesn't mention a you anywhere? wouldn't it be more along the lines of "what kind of hamburger exists"? is the you implied or did i miss something?
It's a cutural/language difference thing at that point. In English, you would never ask "What kind of hamburger exists?" if you were, say, asking this question at a restaurant. So the "you" in that sense is implied in that it is interpreting the meaning of the sentence rather than providing a word-for-word translation.