Must I buy meat or donate money instead of the portion of the Udhiyah that my father took and disposed of, knowing that I do not know the weight or value of the piece, and that my friend, the owner of the Udhiyah, does not know about this?

Your father erred by betraying the trust, and it is obligatory for him to repent sincerely. We advise you to give charity equivalent to the price of the meat on behalf of your father – if you are able – while also advising him to repent. If you do not know the exact amount, then give charity until you are reasonably certain that the obligation has been fulfilled. As for what is legally binding, your father must guarantee this piece because he is the one who caused its damage, and your responsibility was cleared by informing your friend about your father's agency. If you do not wish to bear the responsibility of the guarantee on behalf of your father, then you must inform him of Allah's ruling regarding the obligation of the guarantee upon him. If he does not respond, then inform your friend so that he may demand his right from your father or forgive him.