What is the ruling on taking a person's possessions (phone and a sum of money) after threatening him as a punishment for his demand to commit an immoral act (sodomy)? And what is the correct action to take regarding these possessions?

It is not permissible to access malicious websites, and one must repent from doing so. What you did by threatening this person, taking his ID and the paper evidence he used to collect phone numbers of people he met online, and your communication with his father informing him of his son's condition, is permissible, and it might help save the young man. However, you erred in taking his mobile phone and the money he had with him, and in destroying the documents that could have guided you to his family, because his committing sins does not permit taking his property. These possessions have become a trust in your hands, and you must keep them and search for a way to contact their owner and send them to him. If you are unable to deliver them to him, then you may give them as charity on his behalf and write that in your will. If he comes one day, he has the choice to endorse the charity or take the equivalent of what you took from him, and you will receive the reward for the charity.