Is this act considered unlawful if it involves not distributing the full number of free newspapers as requested by the supervisors and branch manager? Is the money earned from it unlawful and must one dispose of it? And what should the questioner do about it?

If the newspaper owner permits reducing distribution, then there is no harm. Otherwise, hiding copies and not distributing them is considered a betrayal, a waste of money, and a breach of contract, which is forbidden. Repentance for this act is obligatory, by returning the value of the undistributed newspapers, unless the owner forgives it. The manager and supervisors must be advised regarding the prohibition of this action. If they do not respond, or if you fear harm, then inform the highest authority about what is happening. If you are unable to ensure proper distribution, leave the job unless you are compelled to stay, while guaranteeing the value of the undistributed newspapers and searching for another permissible job.