That's not proper English grammar. I feel "What types of hamburger(s) are there?" is closer to what I would use
"What kind of hamburger is there?" is grammatically correct English. "What kinds of hamburger(s) are there?" is also grammatically correct.
At first i had put that as well, Incorrect. I think 무슨 is towards you are another...kind of confused about that as well
Since "hamburger" is the subject, wouldn't it be correct to say "What kind of hamburger is it?"
The sentence doesn't refer to a specific hamburger, so using "this" is out. It also uses 무슨, which means "what kind" or "what type"?