Is it legal to charge a 14 year old rent in a relatives house?
It will depend on the specific situation. The parents are
responsible for the child's welfare.
That's entirely up to you. If you're buying it as a gift, then probably not. However, it's always reasonable to charge rent to a tenant, even if you're related to the person in question. You do not have to charge your son rent. But in the case that you bought the house you have the right to charge him for any space that he is occupying.
Starting on their 18th birthday, technically yes. Parents are responsible for providing for their children until the age of majority (whether they like it or not). As soon as they reach the age of majority (usually 18), the parents can charge them rent, kick them out of the house, or whatever... all perfectly legal (if a tad cold-hearted).