What is the ruling of Islamic law regarding marriage by coercion, and taking birth control pills without the husband's knowledge?

A mature and sane girl cannot be coerced into marrying someone she does not desire. If she is forced into marriage, she has the choice either to accept the husband or to request the annulment of the marriage from a judge, as a virgin bondswoman did with the Prophet, peace and blessings be upon him.

If she cannot bring her case before a judge, she may request a khul‘ (divorce initiated by the wife), while being advised to be patient and not to rush, especially if the husband is respectable and treats her well.

She is not permitted to take birth control pills without her husband's knowledge and permission, as this constitutes an infringement upon his right to procreate. The reasons you mentioned—her dislike for the husband, her fear of poor upbringing of children, or her fear of pregnancy—do not justify preventing pregnancy. Some of these are flimsy excuses or perceived harms that do not contradict the benefit of procreation. She should seek Allah's help and rely on Him.