Is it permissible for a sister to deliver a speech prepared for her by a brother, on the topic of "Women in Islam," before a mixed audience of men and women, and is there any Shar'i evidence that prohibits that?

It is not permissible for a woman to deliver a speech before a gathering of men, except out of necessity, provided there is a barrier between her and them, and that she does not excessively soften her voice; for her voice may be 'awrah (that which must be concealed), and activities must be regulated in accordance with legitimate Islamic guidelines.