Is revealing a sin committed by a girl, at her request, to a small number of friends, which has tarnished her image, considered a sin against people that Allah will not forgive, and how can one seek forgiveness for it if that is the case?

Laughing at the matter of that girl and your talk about her is a sin that necessitates repentance to Allah and asking for forgiveness from the one whose honor you transgressed and whose matter you exposed. If you cannot do that, then seek forgiveness for her. Your speaking about yourself doing that action is boastfulness and openly committing a sin. The Prophet, peace and blessings be upon him, said: "All of my Ummah are safe except those who commit sins openly." So, seek forgiveness from Allah the Almighty and repent to Him with sincere repentance, and seek forgiveness for the sister whose honor you transgressed if you cannot ask for her forgiveness, for that is the expiation for your deed.