Is going to university considered a sin under the mentioned circumstances? And is visiting the mother once a week considered fair? And is it permissible to live with the mother and visit the father, given his health problems and threats of invoking curses?

If a father prevents his daughter from going to university without a valid reason, she is permitted to go without his permission. And if he prevents her from visiting her mother to the extent that fulfills her kinship ties, then there is no obedience to him in that; because obedience to parents is only in what is right and lawful, and honoring the mother is an obligation. And children must serve their father. If leaving residence with the father does not result in his neglect, and staying with the mother is safe, then this is permissible, along with continuously honoring and caring for the father. And if the daughter fulfills her duty of honoring her parents, then the father's unjust prayer against her will not harm her.