Would the failure to marry the daughter of the friend in whose presence the father was slandered, or the failure to invite him to the wedding feast, be considered an act of filial piety, out of fear that the friend might recognize the father? And is it obligatory to inform the friend to correct the image he has formed of the father?

Backbiting is legally forbidden (haram (definition)). Backbiting one's father is a greater sin. The expiation for backbiting is through repentance, remorse, seeking forgiveness (istighfar), supplication (du'a), and praising the person who was backbited with good words. If the backbiting did not reach the person, it is sufficient to seek forgiveness for them and praise them with good words in front of people. However, if the backbiting did reach the person, then it is obligatory to seek their forgiveness and ask for their pardon, unless a greater harm would result from doing so. In the case of greater harm, it is preferable to keep the matter private, frequently seek forgiveness for the person who was backbited, supplicate for them, praise them, and perform many good deeds. It is not advisable to remind your friend of the matter if he has forgotten it; rather, it is sufficient to praise your father in front of him. If a person repents from backbiting, their repentance is valid even if the effect of the backbiting remains.