Is anything required of the questioner, and how can she atone for her sin after her negligence in caring for her sick father, who passed away on the same night?

If you are not certain, or if it is not highly probable in your estimation, that your father died due to your negligence in administering steam to him, then you should not speak about this matter to anyone. Doubt regarding causes holds no weight. If the matter does not exceed doubt, then nothing is incumbent upon you. You should frequently supplicate for your father, seek forgiveness for him, give charity on his behalf, and perform Hajj and Umrah (definition) for him, as the reward for these acts will reach him.