Does what happened—the grandfather's taking possession of his rightful share of the compensation, then giving it to the eldest uncle, and his saying: "I swore, my son, by Allah, there is nothing between me and them; this is money for orphans and I have no claim to it"—constitute a waiver of all his rights in his son's inheritance?

The mere possession of the money by the grandfather is not sufficient proof of his knowledge that it was his lawful right. However, if his knowledge of this is established, and he gave the money to your uncle, the guardian, then this is considered a gift. A specific صيغة (formula) is not required for a gift to be concluded; rather, whatever customarily indicates it suffices. A gift is effected by what people commonly understand as an offer, acceptance, and a mutual exchange that indicates it.