Is it permissible for an employee who has been wronged by having his dues reduced and being given false promises to increase the number of hours on timesheets to ensure he receives his full dues, or close to them? And is it permissible for him to do that to compensate for the end-of-service bonus that was not paid to him due to an administrative oversight, with the manager's knowledge?

If the overtime pay or bonus is due and fixed, and you can only obtain it by increasing the hours in the schedules, then it is permissible for you to do so, provided that you do not exceed your right. This is known as the issue of seizing one's right. This ruling applies specifically to past, established rights that you were deprived of. As for future rights that you fear might be withheld, it is not permissible to claim them in this manner. If the bonus is a gift and not a due right, then it is not permissible to increase hours to obtain it.