Chinese will keep offering the food again and again. It is a matter of custom and shows appreciation to your guests. They do the same with gifts. It is expected that you refuse a few times and your host keeps pleading with you until you accept. It is difficult not to accept a present or an offering of food.
Chinese hospitals are serious places.
I doubt it. My wife is pregnant and we are having midwife deliver the baby. We were asked if we would mind if an intern helped with my wife's case. My wife said of course they can help but only up to a point. After all they have to learn if they are going to help others.