Is the share of the deceased, upon whom the father and uncle spent, considered to have actually transferred to them after the heirs agreed to that, and what is the legitimate distribution of his inheritance?

If a person dies, their inheritance is first distributed to those with prescribed shares. If there are none, it goes to the nearest male agnates (Asabah), according to the Prophet's (PBUH) saying: "Give the Fara'id (prescribed shares) to those who are entitled to them; and whatever remains, is for the closest male relative."

If your deceased cousin did not have heirs with prescribed shares, then his inheritance goes to his nearest male agnates. In this case, your father, your paternal uncle, and the sons of the deceased's paternal uncle are all on the same level of agnatic kinship.

The default is that the inheritance is divided equally among them in this situation. If some of them (the sons of the deceased's paternal uncles) waive their share in favor of your father and your paternal uncle, and they are adult and of sound mind, there is no harm in that. This waiver is considered a gift that becomes binding upon possession, and the land becomes the property of the one it was waived to. Then, after his death, it will be divided as an inheritance among his heirs.