My son is 14 years old. He weighs 115lbs. He has been working out and wants to drink protein shakes. Is this safe for him? If so, what amount?

No. I disagree with my collegues.As pointed out, there is no evidence of any benefit and altho rare, there can be serious side effects such as heart trouble, hypertension, kidney problems, and strokes.And these do occur! why take a chance.
Yes . Though there isn't much reliable research on whey (protein) powder in kids, it is generally accepted as safe. Because of this though, a proper daily amount is difficult to judge. Instead, i usually recommend using one's diet to add protein to the body: milk, lean meats, eggs, and peanut butter are good sources. Kudos for encouraging exercise!
100g of protein per . No benefits accrue beyond 2g per 2.2lbs of body weight, even in professional athletes. No harm if more is ingested, but protein nutritional supplements are expensive. I cannot give a better answer without knowing his weight and height!