Is it permissible for me to live in a house belonging to the municipality, whose bills are paid by them, and can the ownership of this house be transferred to me, knowing that my father obtained it during his work in the same municipality?

The ruling on a son living instead of his father or with him in work accommodation, and paying bills, depends on the condition set by the employer (the municipality). If the employer stipulated that only the worker himself should reside there, then it is not permissible for his son to live with him or in his place, nor to pay the bills. However, if the employer permits it, then there is no objection. If the state grants ownership of the house to the worker, he may accept it and benefit from it. In summary: The conditions set by the employer regarding accommodation, ownership, and bill payment must be observed. Whatever aligns with the condition is permissible, and whatever violates it is not; this is based on Allah Almighty's saying: "O you who have believed, fulfill [all] contracts," and the Prophet's (peace be upon him) saying: "Muslims are bound by their conditions."