Feed is to eat and is physical. Nurture is to feed someone not physically but emotionally and help them grow as a human being or help heal them from trauma

Yes, "feed" usually means specifically to give food to something while "nurture" is to care for something generally/help it grow. You might sometimes see "feed" used metaphorically like to "feed your mind" and in that case it has a similar meaning to nurture.

Yes, there is an enormous difference.