Is the sudden change in my fiancée's behavior, her desire to break off the engagement and leave her studies, in addition to her constant distress and crying without apparent reason, a type of magic, and what is its cure?

What happened to your fiancée is not necessarily due to magic or the like. You should look for apparent causes by consulting doctors. If no organic or psychological illness is found, then it is likely to be magic (sihr) or the evil eye ('ayn). She should perform ruqya on herself, observe the prescribed adhkar (remembrances) and obligatory acts of worship, and avoid sins. There is no harm in one of the righteous people performing ruqya on her, while being careful to avoid magicians and charlatans.