If a child prays for the forgiveness of his/her father who has passed away, regardless if the father was sinful or not, does it only save him in the grave, or will it also save him during the Resurrection Day?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Du'aa’ (supplication, invocation and prayers) is beneficial both for the doer and the one for whom it is done.

Shaykh Ibn Taymiyyah said in his book Al-Fataawa Al-Kubra: “Supplicating for others is beneficial for both the supplicator and the one he supplicated for, even though the supplicator is in a lower rank than the one he supplicated for. The supplication of a believer for his Muslim brother will benefit both himself and the one he supplicated for. Whoever said to another (person) amongst the people: “Make Du'aa’ (supplication) for me", and his intent is to benefit that person commanded to make supplication and to benefit himself as well by that person supplicating for him, then the one requesting this Du’aa’ and his brother whom he asked to supplicate for him are both cooperating in goodness.” [End of quote]

No doubt that Du'aa’ is beneficial during one's life and after his death (in the grave, on the Day of Judgment …).

Ibn Taymiyyah said in his Al-Fataawa Al-Kubra: “Committing misdeeds and sins does not entail entering Hellfire at all unless the following ten reasons become absent: (1) repentance, (2) seeking Allah's forgiveness, (3) good deeds that undo misdeeds, (4) calamities that expiate misdeeds, (5) the Prophet's intercession, (6) other intercession (of martyrs …), (7) Du'aa’ of believers, (8) the reward of good deeds (Sadaqa…) that are done on behalf of a dead person, (9) the trial of the grave, and (10) the horrors and terrors of the Day of Judgment.”

It is indicated in the Quran and the Sunnah that the punishment for misdeeds and sins might be vanished by the ten reasons that we have mentioned above.

Allah knows best.