How many arrows would an archer shoot per battle, what was the average percent of archers in a medieval army?

Many, so much so that they would often run out of arrows – at the Battle of Carrhae, for example, one of the reasons why the Parthian General Surena won so decisively is that he thought ahead and brought thousands of camels to carry extra arrows for his horse archers, allowing them to resupply in the midst of battle. 

As for the percent, it hugely varied depending on time and place and culture. At Hastings in 1066, William’s army was somewhere between 12-33% archers while Harold had almost none. At Crecy, the English army was about 66% archers (including both longbowmen on foot and hobelars, mounted archers), while the French army had only 20% archers and those were Genovese mercenaries. By the time we get to Agincourt, 80% of the English army were archers, whereas the French army was overwhelmingly knights and men-at-arms.