Is it permissible to marry a woman whose engagement was annulled after both parties had developed feelings for each other, and would this be considered an act of "proposing to the fiancée of one's brother"?

A man's friendship with a non-mahram (definition) woman and their exchange of loving conversations are forbidden, and this is a sin that requires repentance. If the recitation of Al-Fatiha was intended for marriage, then she has become his wife, and what you did with her is an act of instigation against her husband, which is a sin. If Al-Fatiha was an allusion to engagement, then it is not permissible for you to propose to her as long as the engagement is ongoing, and it is not permissible for you to cause its dissolution. If the engagement is dissolved, there is no impediment to proposing to her if she is religious and of good character.