Is it permissible to demand compensation for the use of a private car and for extra work not agreed upon in advance when leaving a job?

If you performed tasks outside the scope of your official work and donated them without demanding payment for them either before or after their performance, then you are not entitled to claim compensation for them. However, if you did not donate them and it is customary for someone like you to receive payment for such tasks, then you are entitled to claim fair compensation (ajrat al-mithl).