Is it permissible for the manager to overlook the absence of some employees, or their tardiness, or their early departure, under the pretext of his approval, and is it permissible for the head of the department to grant unofficial leaves or permissions?

If the supervisor is authorized by the employer to exempt employees from attendance, or to permit them to be late or leave early, or to take leave without official documentation, then there is no objection to that. However, if he is not authorized, he is not permitted to do so, nor is the employee permitted to accept anything that contravenes the work regulations, because that is considered a betrayal of trust. Allah Almighty says: "O you who have believed, do not betray Allah and the Messenger or betray your trusts while you know [the consequence]." And the Prophet, peace and blessings be upon him, said: "There is no faith for one who has no trust, and there is no religion for one who has no covenant."