Is a woman required to return the greeting verbally or in her heart when young men enter a mixed-gender university, and is it permissible for her to return the greeting to a boy?

If one of the young boys offers a greeting, it is sufficient for one of them to return it, because returning the greeting is a communal obligation (fard kifayah), and the sin is lifted from the rest if some respond. It is permissible for a woman to return the greeting to a boy; in fact, it may become obligatory for her if no one else responds.