What is the ruling on a girl marrying if she fears and is shy of marriage, intercourse, and childbirth, and she prays to God that no suitor comes to her? Is it permissible for her to marry a man and agree with him to live with him "as a sister"?

A girl should not completely abstain from marriage. If she wishes to marry without cohabitation and without stipulations, she is permitted to do so, provided she feels safe from temptation (fitna) and finds someone who accepts this arrangement. She should, however, be aware that by doing so, she is missing out on much good and the core objectives of marriage. As for her fears, they are mostly illusions. She should resort to prayer (du'a), legitimate Islamic incantations (ruqya shar'iyya), and consult psychiatrists. Her being a doctor does not exempt her from her marital duties. She can reach an understanding with her husband or stipulate her work to him before marriage.