Yes. By all means, breastfeeding will soothe your baby and there is nothing gentler for the infants digestive system than mom´s milk. Most babies have a certain amount of colic that usually subsides by itself by the time the baby is 12 weeks old. As with everything, watch your diet when you nurse.
Yes. Unless a baby seems colicky after breastfeeding, but fine after feeding formula, there would not be reason to stop breastfeeding a colicky baby. If however, a baby seems happy after feeding formula, but colicky after breastfeeding, the parents should see the doctor to look into why the colic is happening.
Yes. Unless there is something in mom's diet that irritates the baby's digestive system, it is quite safe and advantagous to breast feed as long as possible. And if the baby is reacting to something mom is eating then dietary elimination solves the problem. The old "saw" maintaining that mom's diet does not cause discomfort in the baby has been proven in studies not to be true.
Yes. Yes - in fact studies will show that breastfeeding helps with colic as much as anything you can do.