Is there sin upon one who removed a paper of authenticated hadith affixed in the mosque with the Imam’s permission, and a very small portion of the wall’s paint came off, so he returned the paint to its place and left the adhesive to prevent the paint from coming off again?

There is no sin upon whoever removes a paper from the mosque wall, causing damage to the paint, as long as they did not intend to do so. This is based on the Prophet's (peace be upon him) saying: "Indeed, Allah has forgiven my Ummah for their mistakes, forgetfulness, and what they are forced to do."

As for compensation, if the damage was without negligence, there is no compensation. However, if it was due to negligence, then he must guarantee the value of what he damaged, and he should offer the compensation to the mosque officials.