A CHALLENGE FOR US

HERE’S A CHALLENGE FOR US:

1 What is the title of the movie theme song that the sister hums (also hummed by their father’s lover towards the end)?

2 From what Japanese movie was that tune? This was the clue given by the father’s lover to the son

3 Another clue given by the old man is this: The son was named after the main character of that movie. What’s the name of the son?