The second one is correct because it is an embedded or indirect question - a question inside another question. Only the first question has an auxiliary verb or question word order. The embedded question doesn't.

Both are correct. The second has already been defended by others so I will say no more about it. As for the first, it can be defended by regarding the core sentence as "What is the correct answer?" in which the subject is "what", "is" is the verb, and "answer" is the object. Into that sentence, we insert the phrase "do you think" to either modify the verb or merely act as an extraneous thought. Structurally, the sentence is identical to the sentence "What in the world is the correct answer?".

The second one is correct. Don't invert the subject and verb in imbedded questions, only in direct questions: What is the correct answer? Can you tell me what the correct answer is? I would like to know what the correct answer is.