Is it permissible to complete a free diploma study after ceasing to teach at the university, knowing that the university may not allow non-employees to study, but no official order has been issued to that effect and the name is still listed?

If you were nominated for this diploma while working with the university, and your name was then included in the list of students for this year, despite your cessation of work, there is no harm in you completing your studies, because it appears that the university is aware of this and has given its approval. However, if you were to consult the relevant administration, it would be more absolving for your conscience.