What are you doing home? (=Why are you at home?)
-> 为什么在家呢？

it can mean anything you want. but why this?
that question isn't asking why that person is home.
asking what that person is doing at home..

It is not asking what that person is doing at the moment while they are inside their home. At least, not in English. The wording would have to be different to imply what you are assuming. The English is ONLY asking WHY they are at home. So "Evde ne yapıyorsun?" and "你在家做什么？" are incorrect translations (of the English sentence).

in this Chinese sentence, it's not asking "why"
you are making comments on wrong page.

No, the comments are on the right page. Please pay attention to the contents of the comments.

The English sentence, which this sentence is linked to, is asking "why".
As the Chinese sentence does not do so, this is an incorrect translation of the English sentence. This is what the comments allude to.

This Chinese sentence is a valid translation of the Turkish:
"Evde ne yapıyorsun?"
but is not a valid translation of the English:
"What are you doing home?"

So, either the Chinese sentence can be changed to correspond to the English sentence, or, it can be unlinked. Since the Chinese sentence is a valid sentence, I will simply unlink this sentence from the English sentence, I think there is enough in the comments of this sentence to understand the reasons why this must be done.