Does a person who was not appointed to a public position, despite being entitled to the appointment by law, deserve compensation due to a success criterion in the competition announcement that violates the law? And is the competition announcement considered a binding contract?

It is permissible to accept compensation if the law does not contradict Sharia, and the standard (for the competition) was deemed invalid, and the person was qualified for the position. However, if the law contradicts Sharia, it is not permissible to accept compensation, and the competition standard remains the one to be considered, likewise if the person was not originally qualified for the position.