Is it permissible for a Muslim to listen to the Qur’an recited by a non-mahram woman, and does the same ruling apply when meeting a girl for engagement purposes?

It is permissible for a man to listen to a woman's recitation of the Quran, provided that her voice does not contain elongation or softness that could lead to fitna (temptation) and pleasure. The voice of a non-mahram (definition) woman is not considered awrah (nakedness) according to the more sound opinion, but it is forbidden to derive pleasure from listening to it, even during a recitation. There is no difference in the ruling between a fiancée and other non-mahram women.