How do I restore people's rights, such as injustices and money taken unlawfully, especially to those whose whereabouts or condition I do not know? And is the restoration of injustices exclusive to believers or does it apply to all people?

Rights must be returned to their owners, whether they are Muslims or non-belligerents. If the owners cannot be reached, then material rights should be given as charity on their behalf, and for non-material rights, abundant supplication should be made for their owners and good mention of them should be made in the gatherings where they were wronged. If you do what you can, and Allah knows your sincerity and your inability, then Allah may take it upon Himself to repay those rights on your behalf. This is based on the Almighty’s saying: "So fear Allah as much as you are able," and "Allah does not burden a soul beyond its capacity." This must be expedited before the Day of Judgment, when the wrongdoer's good deeds will be taken for the wronged, and if his good deeds are exhausted, then the sins of the wronged will be taken and placed upon him, after which he will be cast into the Fire.