I had a female class-mate when I was studying in middle school, but praise be to Allaah I adhered to the words of the Prophet (peace and blessings of Allaah be upon him) which say that one should not be alone with a non-mahram woman. My question is: I know that she has some good characteristics, and I want to offer her advice and guide her, but the Prophet (peace and blessings of Allaah be upon him) forbade being alone with a non-mahram woman, and Allaah forbids looking at a non-mahram woman. So how can I call her (da’wah)?.
As you mention, it is haraam to be alone with a non-mahram woman and it is haraam to look at her. If you want to offer her advice, then you can speak to her when she is concealing herself from you, and without being alone with her. You could also give her some useful books and tapes that will help her to learn the rulings of her religion, or write the advice to her, or use other useful means that will not lead to fitnah and will achieve the desired goal.
And Allaah is the Source of strength.