Is it permissible to give one's son to his maternal grandfather's house to raise him? Can he call his grandfather "father"? And is there a reward for that?

It is permissible to entrust a child to someone who will raise and sponsor him, or to someone with whom he finds comfort. This may be an act of benevolence. However, the parents must monitor his affairs, care for him, and ensure he is raised properly. There is no harm in him calling his grandfather "father," because a grandfather is a father.