How did the taxi driver know that the girl knew someone else, and why did he say to her what he said, and was a jinn speaking to her, and what is the religious ruling on that, knowing that she was menstruating at the time?

The questioner and the girl erred by secluding themselves, going out for recreation, and talking. She also erred by secluding herself with the driver if no one else was with them. They both must repent. As for the driver's knowledge of the matter, there is nothing strange about it; he might have learned about it from the person himself or from someone else.