Is it permissible to perform Hajj on behalf of a person suffering from severe epilepsy and urinary incontinence, especially if he owes a large debt to his siblings and they have forgiven him for it?

For Hajj to be obligatory, financial and physical ability are prerequisites. If someone is ill with an incurable disease, and traveling and performing the rituals would cause them severe hardship, then Hajj is not obligatory upon them personally. However, they must appoint someone to perform Hajj and Umrah on their behalf if they possess sufficient funds for it. If they do not possess the funds, then Hajj is not obligatory upon them. If the illness is expected to subside, then they must wait until Allah cures them.

As for your brothers' permission regarding the amount you took, it does not affect the ruling on your Hajj.