Is it permissible for the one who fulfills a vow to eat from the sheep vowed for the poor and needy after his father's recovery, and is it permissible to bring the sheep cooked from a restaurant, and is it permissible to fulfill the vow on one of the two Eids?

The vow must be fulfilled in the manner in which it was vowed, for the Prophet, peace and blessings be upon him, said: "Whoever vows to obey Allah, let him obey Him."

Therefore, you are obligated to slaughter a sheep for the poor and needy after your father's recovery. Bringing a slaughtered sheep instead will not suffice. It is not permissible for you or anyone else who is not poor or needy to eat from it. There is no objection to fulfilling the vow on one of the two Eids or at other times, unless a specific time was designated for the vow. Hastening to fulfill it is more preferable.