How can one get rid of lust while talking to his fiancée, and is what he is doing wrong? And how should he deal with his fiancée's friend who proposed to her and she rejected him? And what is the stance on his refusal to live in the apartment that the girl's father designated for her?

It is not permissible to listen to the words of a non-mahram woman with lust, nor to speak with her except out of necessity and with assurance against temptation. There is no obligation to seek permission from the young man whom the girl rejected when she becomes engaged. The questioner is not obliged to live in the apartment gifted to the wife, nor does he have the right to prevent her from accepting her father's gift. His refusal to live there should be done with wisdom.