Is it permissible for a man to add a foreign woman who is adorned (showing her adornments) to his private Facebook profile or to look at her picture, under the pretext that the picture is small?

It is forbidden for a man to look at a picture of a woman who is unveiling herself and is a stranger to him. Therefore, it is not permissible to add an email address that requires displaying an unveiled picture. It must be noted that Islamic rulings are derived from the Qur'an and Sunnah, not from the actions of men.