"Why does she study?"
Translation:वह क्यों पढ़ती है?
No, it is grammatically incorrect. :) All question words need to be placed after the subject!
The only instances where a question word is placed at the beginning is when it is not a direct What/Why/Where/Who/How question. And the only question word used in such a situation is "क्या" (typically used for "what?"). That is the correct sentence structure for such indirect questions. For example, "क्या वह पढ़ती है?" - "Does she study?" Here "क्या" is used to make a question out of "वह पढ़ती है" - "She studies", and not for anything related to "what".