The Wolf could probably answer your biting question better than I, but I think the problem is just the normal pecking order being established. Zebra Danio's usually have a dominant female that is the "leader" of the group. When first put into a new setting the females will nip at each other until dominance is established. You will also see a bit of nipping sometimes when the male and female are ready to mate. As long as you are not seeing any real damage to the fish or fins, they will work it out among themselves and be fine. Once they settle down you will enjoy watching them school. It amazes me when I watch mine twisting and turning in a tight little knot and never running into each other.
eudielynn has already answered this
It is a pecking order thing and nothing to worry about
I won't harp on about the tank size and useing ZD's to cycle a tank
as others have already said about it.