Is it permissible for a doctor to complete his studies abroad with money from his father, which the father received as compensation from a company, and he paid a bribe to an employee to facilitate its receipt? And is it permissible to take this money as a loan?

If your father is entitled to the compensation amount, then there is no harm upon you in dealing with him with this money, whether as a gift or a loan. You are not affected by his payment of a bribe to obtain his right, as he does not sin by paying it if he cannot obtain his right except through it.