Is it permissible to defraud an unjust employee, and to seek help from relatives who caused him financial loss?

The questioner is not responsible for his relative's loss. Whether he is at fault depends on knowing the trick he used with the supervisor. However, merely seeking help from a relative to speak to the supervisor so that he is not wronged is not a mistake. The supervisor must fear Allah and be just, and it is not permissible for him to inform some individuals about the exam topics, just as cheating in exams is not permissible.