Is it permissible to take money from the university for being appointed as an examiner for a division in which nothing has been examined, and what is the amount that may be taken if the answer is in the affirmative?

If grading materials requires your presence for specific working hours, then you are entitled to payment simply by making yourself available for work, whether or not actual work was assigned to you, because a private contractor is entitled to their wage upon making themselves available. However, if the work does not necessitate your presence, but rather is done elsewhere, then you are not entitled to payment except upon completion of the work. It is not permissible for the course instructor to claim that you performed work contrary to the reality, as this is a lie and consuming wealth unjustly.