Will using norditropin (human growth hormone) make a teenager grow taller?

Not significantly. Kids with short stature need an evaluation by a pediatric endocrinologist to see if they are hormone deficient, late bloomers or just genetically short. There is no firm evidence that supplemental growth hormone will add inches to the final height of a kid with normal levels. It may push him to his genetic max sooner at a cost in excess of 10K/yr.
Not for them. This is really for children who have a deficiency in growth hormone, and short stature for noonan's syndrome, turner's syndrome, and no catch-up growth by 2-4 years. It is also for adults with low growth hormone and other hormones, and those with low growth hormone as a child. It is apparently not for teenagers. It might make a short adult grow taller, but may need dose adjustment if grown.