Is meeting with women in restrooms, or with library officials, considered a gathering that necessitates giving advice, or is giving advice limited to those sitting next to me only?

Enjoining good and forbidding evil is one of the great rites of Islam. It is permissible in public and private gatherings. It is obligatory when one sees something forbidden or the abandonment of an obligation. It is recommended when one sees something disliked or the abandonment of something recommended, provided one has the ability to enjoin/forbid and there is no fear of a greater corruption.

General advice and guidance for women present, reminding them of Allah and the virtues of good deeds, even if there is no specific wrong that necessitates forbidding, is a good and desirable act, and it falls under calling to Allah. It is a condition that the caller (da'i) be knowledgeable about what he is calling to, based on the words of Allah Almighty: "Say, 'This is my way; I invite to Allah with insight, I and those who follow me.'" (Surat Yusuf, 12:108) And His words: "And who is better in speech than one who invites to Allah and does righteousness and says, 'Indeed, I am of the Muslims.'" (Surat Fussilat, 41:33)