1) How well do you think YOU WOULD manage in an emergency situation?
We have here two clauses.
How well do you think ---> Do you think? Modal Subject Verb, the other bit is an adverbial.
You would manage in an emergency situation. --> You would manage.
Clause one is a question, formed using the modal do.
Clause two is not a question but a statement.
To make a question out of it, turn you and would around. ( no, not uoy and dluow! (little joke))
Would you manage?
So the 2) above is wrong, because you already asked a question 'Do you think?' and promptly proceeded to ask another without a question mark or an answer to the first question. At the very best, that is messy writing.