Are the sums distributed as incentives from student fees permissible, even if they were not shown in the accounts, and what is the ruling on sharing the surplus amount found in the fund?

The funds that were taken with the knowledge of the university director and did not appear in its accounts: their permissibility depends on the director's authorities granted by the university owners. If he was truly authorized to distribute them, then there is no harm in taking them. Otherwise, they must be returned to the university's account because they were taken unlawfully, along with repentance. As for financial surplus or deficit, refer to Fatwa (definition) No. 59095, which states that an accountant or treasurer is not liable for a deficit unless he has been negligent or transgressed.