Is it permissible to take out a loan from an interest-based bank to pay for university tuition fees in Norway, or should one abandon their studies?

It is not permissible to take a loan with interest (riba) except in cases of dire necessity recognized by Sharia, and studying is not one of them. Usury (riba) is forbidden and is among the major sins, as the Prophet, peace and blessings be upon him, said: "Allah curses the one who consumes riba, the one who gives it, the one who records it, and the two witnesses to it… they are all equal in sin." Therefore, it is forbidden for your cousin to take an interest-based loan to study medicine, even if it leads to her dropping out of her studies.