What is the way to get rid of a guilty conscience and feel at ease after having uncovered the face to a policeman when preparing the national ID card? And is this sin considered a cause for torment and failure in the religion exam?

The matter is easier than you imagine, for you may not be sinful if you uncover your face out of necessity or need. Even if you were sinful because there was no need, repentance erases what came before it, and the one who repents from a sin is like one who has no sin.