I am not real sure on the answer to your first question, but i would presume that the cord would fully stop pulsating before the placenta is birthed whether naturally or not. No. 2 i think they would still need to tug on the cord a little for it to come out, i know with me i was given the injection and think this happens while you are birthing your baby, that they pressed on my belly a couple of times and them tugged on the cord a little and then the placenta was delivered. Didn't hurt in the slightest. No. 3 you might get a bette answer from someone else as i have never engaged the services of an OB and as such the middie does all the work.

Hope i helped a little