Is it permissible for a student not to attend examinations in order to benefit from the university's insurance for an additional year due to her need for expensive medications after a kidney transplant? And is it permissible to use her sister's insurance card in this case?

If the university regulations do not permit delaying an exam due to health conditions, then it is not permissible to delay it to obtain additional insurance. This falls under deception and consuming people's wealth unlawfully, which is forbidden in Islamic law. Allah (the Most High) says: ﴿And do not consume your properties among yourselves through falsehood﴾. And the Prophet (peace and blessings be upon him) said: «Whoever deceives is not of me.»

However, if the university regulations permit this, then there is no harm, as the university is the rightful owner (of the decision).

As for using the sister's insurance card, it is not permissible due to the forbidden deception and forgery involved.