Is it permissible for a woman to look at a non-mahram man with the intention of discerning his character and demeanor in preparation for marriage, or does that fall under the whisperings of Satan?

A woman must lower her gaze from 'awrat (private parts) and forbidden things. It is unlawful for her to look at men with lust or fear of temptation, based on the Almighty's saying: "And tell the believing women to lower their gaze." It is permissible for a woman to look at what is ordinarily visible of men, such as the head and arm, provided it is not with lust, pleasure, or fear of temptation, relying on Aisha's hadith and her looking at the Abyssinians, and the Prophet's saying to Fatimah bint Qais: "Spend your 'iddah at the house of Ibn Umm Maktum, for he is a blind man and you can put off your clothes in his presence." As for looking for engagement purposes, it is permissible if there is a firm intention to propose, after which the ruling reverts to that of other non-mahram men. It is advisable not to look before engagement to prevent temptation.