Yes. Young babies may spit a little milk out the nose, when spitting up out the mouth.
Yes. The way your baby's stomach, esophagus, back of throat and back of nose are connected is much more of a straight line than it is when you are an adult. So yes, when stuff comes up from the stomach, it is pretty much a direct line out the nose!. As your head grows and your facial structure changes, it is more likely to end up in your mouth but with the right position, could still come out your nose.
Yes. Although it may look very serious, your baby is suffering from a common problem. Gastroesophageal reflux (ger) occurs in more than half of all babies in the first 3 months of life. You can treat it by thickening feedings with 1 tsp of rice cereal to 2 oz formula and holding your baby upright during and after feedings. Your doctor may try medication if these treatments aren't enough.