Is it permissible for a Muslim woman to initiate or return greetings of peace (salam) to men who are not her mahrams, and to converse with them, according to the Shafi'i school of thought, and does the ruling differ based on the man's age?

It is forbidden for a young woman to initiate greetings (salaam) to a non-mahram man or to return his greetings. It is disliked for a non-mahram man to greet her or return her greetings, unless there is no fear of temptation (fitna). As for an old woman, it is permissible for her to initiate greetings and return them. It is not permissible for a non-mahram man to offer condolences to a young woman; rather, her mahrams and her husband should offer her condolences. If greetings and condolences are prohibited, then it is even more so prohibited to converse with her, except when there is a need and no fear of temptation.