Is it permissible for one of the living brothers—who has already performed Hajj for himself—to perform Hajj on behalf of one of his two deceased brothers who were killed, using the money that the parents received as blood money or compensation?

There is no objection to one of the brothers performing Hajj on behalf of two deceased brothers from the blood money, provided that the pilgrim has already performed Hajj for himself. This is because blood money is permissible wealth for the heirs. It is permissible for every legally responsible heir to perform Hajj from their share of the blood money. If the two deceased individuals were capable [of performing Hajj] but did not do so, then performing Hajj on their behalf from their estate is obligatory.