Yes! This is instinctual behaviour, as in the wild when the puppies were reading to be weaned off milk, the mother will regurgitate and feed her puppies. If you watch, the puppies will jump up and lick at the mothers face and mouth, this triggers her instincts to feed. I would suggest taking a high quality puppy food, grind it up in the blender, and add enough warm water to make a soft meal, like the consistency of oatmeal. If you do not have a blender, soak the puppy food until it is soft and mushy. Usually this will help to inhibit the mother's need to feed her puppies. For more information on puppies, health, training and feeding, see my profile on liveperson.
Yes, she is probably regurgitating food to feed them. Puppies usually start eating puppy food when they are 3 weeks old