Hi Sazz
Usually they will give you the syntocinon as the babies head is being born. You could, and have every right to insist that you are not given the injection of syntocinon unless there is a medical emergency.
The gas does cross the placenta, however the gas is out of your system ver quickly. In fact when you stop breathing the gas it is out of your body and therfore not having any efect on you or your baby within a couple of minutes or so.