you *did* log in, that was actually a response for a successful login right there.
as far as subsequent requests go, you need to use that cookie information and send it back to the browser with each request you make (the point of cookies). Yes, you must store and send back all of the data in those Set-Cookie headers... each one. If you don't, facebook has no way of tracking your previous request and can't detect that you are indeed logged in-- even though *you are*.
