Chacham Ovadia writes in Yabia Omer 1:6(end of section 7) different opinions on listening to a woman's voice without knowing what she looks like. He brings the gemara in Berachos 57b that says: three ...
A woman should not sing along to a song in the presence of unrelated Jewish men. But can she mouth the words? I never see frum women doing this, presumably because of marat ayin. As far as the issue ...