Is there a height where my 15yo qualifies for HGH to increase his height?

Complicated. Absolutely speaking, if a boy is less than -2.25 sd on height chart or - 2 sd below mid-parental height and if his growth plates are still open , then he deserves a thorough evaluation quickly to determine if he can be helped.
Growth plate. Is all depends on the bone age of state of maturation that your child bones are if the growth plate is still open you can still use hgh.
Not exactly . 15 yo boys often have delayed puberty which sets back the timing of sexual maturation, therefore also delaying the pubertal growth spurt. If the problem really is gh related then there is no height requirement necessarily. Such concerns merit an appointment with your son's pediatrician who can help to determine if a sub specialist should be consulted related to concern of a growth disorder.
Yes, in a few cases. In a few cases, a boy at age 15 years may qualify for growth hormone injections to try to increase height. But most 15 year-olds are finishing their height growth (growth areas in the long bones are closing) and would be unlikely to benefit from growth hormone. The "minimum normal height" predicted for a boy is 2-3 inches below the "mid-parental height" of: 0.5 x (dad's height + mom's height + 5).