"Are there many Kurds in Turkey?"
Translation:Türkiye'de çok Kürt var mı?
I am learning Turkish too, so I am not quite sure, but I think birçok only can be used here in the case that there is following a second part of the sentence, such as: Türkiye'de birçok Kürt Türkiye'nin batısında yaşar. Otherwise you will have to use "çok". May anybody correct me If I am wrong.
Var/yok applies to people as well. I can think of 3 reasons why your answer is marked incorrect:
1) You wrote "mi" instead of "mu"
2) The answer is forgotten to be added.
3) The alternative translation is not as natural/idiomatic as the original. It is certainly understood but deep down it may not even be grammatically correct, I'm not sure. The original sentence represents basically how this is normally asked.