New Zealand's first gold medal in Olympic athletics (track and field) was won by Jack Lovelock in the 1936 Olympic Games in Berlin. He won the 1500 meter race in what was then a world record time of 3:47.8.
Yes, by Jack Lovelock in the 1500 meter run.
New Zealand's first Olympic gold medal was won at the 1928 Games in Amsterdam by Ted Morgan in boxing in the welterweight division.
India won the Gold Medal of the Field Hockey of the 1928 Olympic Games.
That was Harry Kerr who won the bronze medal in the 3,500 meter walk at the 1908 Games in London.
India's first gold medal came in field hockey at the 1928 Games in Amsterdam.