Since the woman gave the man $5 at the end of the story, we can guess that she didn’t know the answer to her own question.
The woman and man had met each other previously is incorrect. There is nothing in the passage to suggest that the man and the woman knew each other prior to the flight. We can assume that they met as strangers.
The man did not really want to play the game with the woman is incorrect. The man obviously wanted to play the game with the woman or he wouldn’t have offered her $500 if he couldn’t get the right answer.
The man cheated when he tried to use his laptop to find the answer is incorrect. It’s true that the man used his laptop to try to find the answer to the woman’s question. But this was not mentioned or implied as being against the rules.