Is it permissible for me to publish information that harms a person who caused me material and moral losses, in order to obtain the money he promised me, and is this money considered rightfully mine?

You are not permitted to publish what has come into your possession about the man in order to obtain the money he promised you. The money is his property, and you have no right to it on the pretext that he broke his promise. If you have a right against him and he denies or procrastinates, you can sue him before the Shar'i (Islamic) judiciary to examine the truth of the promise and its enforceability. However, taking his money by threatening him with people who would harm him is not a legitimate way to claim a right.