Is it permissible for a nurse to take medicine worth 1000 Riyals from the hospital pharmacy and give it to a poor patient, knowing that the nurse says he does it for the sake of Allah?

Your father is not permitted to take medicine from the hospital unless he is authorized to do so, because that constitutes an infringement on the hospital's right. If he wishes to help people, he should do so with his own money or through his intercession. What he is doing is Islamically forbidden, because Allah is good and accepts only what is good. A good intention does not justify an unlawful means. It was mentioned that Abu Hanifa was asked about someone who steals in order to give in charity, and he replied that his theft is recorded as a bad deed, and his charity is not accepted because Allah is good and accepts only what is good.