What must be done for my father to be credited with the reward of Hajj after his death, as he had the intention of performing Hajj? And can the costs of his Hajj be donated to my needy maternal uncle who will accompany my mother?

If your father was able to perform Hajj previously but did not, then the cost of Hajj should be taken from his estate, based on the hadith of Ibn Abbas: "Fulfill Allah's debt, for it is more worthy of being fulfilled." However, if he was not able and died before the time for Hajj arrived, after he had started the procedures, then you are not required to take anything from his estate for Hajj on his behalf. Nevertheless, you may perform Hajj on his behalf or pay someone to perform Hajj for him, after the heirs agree, provided that the one performing Hajj on his behalf has already performed Hajj for himself.