What are the imediate risks and first steps for this situation:
while chasing another student on the trail, a boy fell and cut himself on the jagged rock. the cut is deep and bleeding won't stop.

Apply pressure with a clean cloth or towel to slow bleeding down evaluate
if it's deep enough for stitches. You can usually tell if a bandaid won't hold the skin together 
If it's deep enough for stitches head to the Dr. or emergency room

Cotton with iron probably