It is not permissible to correspond or converse with a non-mahram woman. If a man intends to propose marriage then he should follow the Islamically-prescribed means of doing so. If the woman whom he wants to marry is one of his relatives, then it should be more straightforward because either he will knows about her or he will be able to find out about her from the women of his own family.
It is not possible for a man or a woman to find out about the real character of one another through correspondence and conversing before marriage, because neither of them will show anything but their best side.
Shaykh âAbd-Allaah ibn Jibreen was asked:
If a man corresponds with a woman and they fall in love, is this regarded as a haraam action?
This action is not permitted, because it provokes desire between them and makes them hope to meet and get in touch. This often leads to temptation and sows the seeds of zina in the heart, which leads to immoral actions or the things that lead to them. We advise all those who want to protect themselves to avoid corresponding and the like, so as to protect their religious commitment and their honour. And Allaah is the Source of strength.
Fataawa al-Marâah al-Muslimah, 2/578, 579
We have already stated that correspondence between the two sexes is haraam, in the answers to questions no. 26890 and 10221.
It is permissible for the man who has proposed marriage to look at his fiancÃ©e, without being alone with her or shaking hands with her. So you could do the marriage contract and delay consummation of the marriage, so that your meeting with her will be acceptable according to shareeâah, and during this period you could focus on getting to know her more and more.
In the answer to question no. 7492 there is an important discussion of this matter.
See also the answers to questions no. 7757, 2572 and 20069 to find out more about the limits of the relationship between a man and his fiancÃ©e. And Allaah knows best.