Is it permissible to use Zakat funds to cover university expenses and the needs of a debtor who supports two university students, given his difficult financial situation?

If your agency in distributing Zakat (definition) is absolute and no specific category for disbursement has been assigned to you, then you may take from it if you are among its eligible recipients, such as being in debt and unable to repay your debt (Gharimah), or being poor, or needy. This is the more preponderant opinion. However, if you are not an eligible recipient of Zakat, then it is not permissible for you to take from it, and you must distribute it. As for taking from it to pay for your daughters' university expenses, it is not permissible except under specific conditions, and the more cautious approach is not to take from it to pay tuition fees.