Who determines the harm that waives the obligation to obey one's parents: the child or the doctor? And is obedience waived merely by the fear of harm occurring, or is certainty required?

Obeying parents is obligatory in matters that benefit them and do not harm the child. The harm considered is significant harm, not minor. If the child predominantly believes that parental pressure increases their illness, then obedience to them is not obligatory, and they are not permitted to cause him harm. The child must deal gently and kindly with his parents and seek help from Allah and from those who have influence with them to alleviate the pressure, while striving to obey them as much as possible due to their immense status.