What is the ruling on money that has been mixed with the agent's money and disposed of by him with profit and loss? Do the heirs have the right to claim what they renounced? And are the profit and loss rightfully theirs, or do they only have a right to the original amount?

As an agent for the heirs in collecting installments from debtors and depositing them into their account, any other disposition of their funds is considered a breach of trust, entailing sin and liability. If you invested their money in your trade and incurred a loss, you are liable for it. As for the profits, the most equitable opinion is that they should be equally divided between you and the heirs. You must review the accounts and reconcile with them regarding the profits, knowing that their share of the profits follows the principal amount and should be returned to the heirs' account. Your brother's anger at your disposal of his share without his permission is justified, and you must repent and seek forgiveness from the heirs. As for the brother retracting his gift, it is not permissible according to the majority of jurists. In summary, any remaining funds of the heirs must be preserved and not disposed of without permission, half of the investment profits are yours and the other half belongs to the heirs, and the brother cannot retract his gift.