Is it permissible to abort a pregnancy resulting from rape before the fourth month, and is it permissible to marry the woman who conceived it before she gives birth?

The woman was right to refuse to abort her fetus, as abortion is impermissible, even before the ensoulment. The mere fact that the pregnancy resulted from rape does not permit her to abort it.

She should be careful in the future and take the necessary precautions. Her marriage will help her in this regard.

It is not permissible for you to marry her before she gives birth, due to the obligation of 'istibra' (ensuring the womb is clear). If you are able to marry her after the 'istibra', that is good and commendable, as it helps her to maintain chastity. What happened to her should not be an impediment to your marrying her.

If you do not wish to marry her, or fear that the marital life would not be lasting, then work on helping her find a righteous man who will marry her.