How can a father who takes zakat for himself be reminded that this is not permissible, what is the expiation for that, and is zakat al-fitr permissible for a poor university student?

A father who is not poor is not entitled to take money designated for the poor. His action is considered a betrayal, a dereliction of trust, and an injustice to the needy. You should advise him wisely to repent and return the money to those who are entitled to it, or to its owners if he cannot find poor people. However, if the father is poor, he is permitted to take from it if he is eligible for zakat (definition), unless the owner of the money specified a particular entity or person. It is permissible to give zakat al-fitr and other forms of zakat to a university student if he is eligible.