Is laughing or what was done considered mockery of God or the Qur’an, and is it necessary to repent from that feeling of depression?

It is advisable to disregard whispers of mockery, and the laughter mentioned is not mockery of the Qur’an. As for ridiculing the sister, it is forbidden by Islamic law, based on the Almighty’s saying: "Let not a people ridicule [another] people…" (Qur'an 49:11). Therefore, the questioner should frequently seek Allah’s forgiveness and perform righteous deeds, and generally repent from sins, in accordance with the Almighty’s saying: "But whoever repents after his wrongdoing and makes amends, indeed, Allah will accept his repentance." (Qur'an 5:39). It is obligatory to treat the sister kindly and seek her forgiveness, for regret over a sin is repentance, and sadness is a sign of regret. Sincere repentance and a firm resolve to guard one's tongue and seek the sister's forgiveness are necessary; by doing so, the repentance will be accepted, by Allah's permission.