If the orders from the health ministry are that the medical examination should be done for free, and donating blood is voluntary, then the blood bank has no right to withhold the examination or to force anyone to donate his blood.
Withholding the exam and forcing the one who wants it to go to a private hospital and pay money for that, is wrongdoing and transgression, and the blood bank is falling short in its duties by doing that.
You should check with the administration of the blood bank and remind them to work in accordance with the instructions issued by the ministry. If they respond, then praise be to Allaah. Otherwise, you should refer the matter to those who are in charge of health, so that you will be free from blame.
You should adhere to the working hours that have been agreed upon, and it is not permissible to sign in and then leave at a time other than the real time, because that is lying and betrayal.
If the administration of the blood bank has decided to reduce the working hours and has stated that the workers on the day shift may leave at 3.30 for example, there is nothing wrong with that, so long as it does not adversely affect the work. But they should speak to those who are in charge in the ministry of health and ask them to change the working hours, so that employees will not be in a confusing situation if they leave an hour before the regular time, but if they stay, they will be doing nothing.
And Allaah knows best.