Yes. This poses no health risks to the baby, but keep the volume low as the sound and lights may distract the baby from nursing well. Make sure you continue to pay attention to your baby, they will be giving you cues as to when they are done, if they are comfortable, etc. Nursing is a great time to bond with your baby so just make sure you don't tune out completely with the tv!
Kind of, sort of... Sure, if the volume is low and you're not too close to the tv, it's not physically harmful to your baby...But what a missed opportunity! news, sit-coms, and movies will come and go, but you're developing a bond with your baby that will last a lifetime. Focus most of your energy on that little munchkin and you'll reap the benefits for years to come.
In moderation. You can watch tv while nursing, but don't miss this very special time to interact with your baby. She will be gazing at you, and your face with be in focus in this position. The light, sound and activity on screen may be distracting to older infants-in that case turn it off. It's preferable to use this time to sing, say nursery rhymes, or just talk to baby-about anything and everything! enjoy!
Sure. The american academy of pediatrics has recommended limited or no tv under 2 years old. There are many many better ways to stimulate your baby's development. The tv should not be a substitute baby sitter. However let us use some common sense. Moderation of most things is never a problem. If the baby is truly hungry, they will not be distracted. I can not imagine this to be a serious problem.