Is it permissible to perform the funeral prayer over the father's grave to seek mercy for him? And does the deceased receive a reward if he bequeathed a Mus'haf (copy of the Qur'an) and his children recite from it?

If you prayed over your father with the congregation, do not repeat the prayer. Rather, visit him and supplicate for him at the grave, and supplicate for the Muslims and believers, as the Prophet, peace and blessings be upon him, taught us. However, if you did not pray over him with the congregation, then you may pray over his grave within a month or less. But if a long time has passed, then supplication, seeking forgiveness, showing mercy, and giving charity on his behalf are what will benefit him. The Qur'an left by the deceased benefits him if it is endowed, as do scholarly books or anything from which people benefit. Enduring charity, beneficial knowledge, and a righteous child who supplicates for the deceased are all matters that benefit the deceased.