Is it permissible for an agent entrusted with managing the property of heirs to profit from it and take a percentage of the rents as his fee, and is it permissible for him to carry out this work without a commercial registration?

Your father's office is part of his estate, and its profits belong to the estate, while the person working in it is entitled to a wage. You may take a salary for your work with the agreement of the adult heirs. If there are minor heirs, then take what is reasonable and according to need, for Allah Almighty says: "And whoever is rich, let him abstain; and whoever is poor, let him eat in a reasonable manner." Working without a registration is permissible under Islamic law, unless the ruler mandates obtaining it for the organization of public interests, in which case it must be adhered to.