Does the Hadith "It is not permissible for a Muslim to abandon his brother for more than three (days)" apply to a male colleague and a female colleague at work (of the opposite sex) regarding the greeting, and does discord between two brothers in a study circle affect the reward of those present, and what is the ruling on one who is lenient in reconciling between two brothers?

Giving salutations (salaam) is encouraged, not obligatory. It is permissible to give salaam to a non-mahram (definition) woman if there is no fear of temptation (fitna). The forbidden abandonment (hajr) is that intended for severing ties, not the absence of salaam due to not meeting or fearing fitna. Discord between two individuals in a study circle does not affect the reward of those present in the circle, but it delays forgiveness for the disputants. Reconciling between people is encouraged by Islamic law and may be obligatory for whoever can influence the disputants to prevent fighting or severing ties of kinship.