Answer:
because its a question and not a stetement
Explanation:
yes you could put ella before va but that would make it a statement. So in order for the sentance to be a question they put ella after estudiar.
Answer:
It is correct to say that, I think it is even more correct/native to say the second phrase.
And the second question, I don't really know it. I'm spanish, but I would never say '' va a estudiar ella en a biblioteca hoy'', I would say '' ella a a estudiar hoy en la biblioteca''.