Is the aforementioned scriptural marriage considered valid, and what is the ruling on the rape of a girl and her subsequent pregnancy, and what must she do regarding the fetus and her paternal cousin according to Sharia?

The marriage that took place is invalid due to the absence of the Shariah conditions. The girl and her family must repent for their sins and regret what happened, and she should inform her family of what occurred while being discreet about her. It is not permissible to abort the pregnancy except for a legitimate Shariah reason and within very narrow limits, while taking into consideration the danger this poses to the mother's life. It is not permissible for the fornicator to marry the woman with whom he fornicated except after their repentance and after she has given birth.