بسم الله الرحمن الرحيم
(1 & 2) The said person should return all the money (bribe etc) which he took illegally to their real owners if he remembers them; otherwise he should give it in charity on their behalf. The details of using the money by his children is that if he has mixed the income i.e. lawful and unlawful both types of money and the lawful income is dominant then it shall be right for the children to use them. But if the haram and unlawful income is dominant then it is not lawful for the children to use it.
(3) The ruling shall be the same which is mentioned above in case of taking the money as loan.
(4) In case the owners are known then it shall not be sufficient to give the money in charity.
Allah knows Best!
Darul Uloom Deoband