Is it permissible to marry a girl who has been religiously engaged, and the Istikhara prayer was performed without any specific outcome appearing regarding her, but the suitor is not convinced by her beauty as a wife for him?

The expansion or contraction of one's chest after Salatul-Istikhara should not be heavily relied upon; rather, it is a feeling that can be considered when deciding whether to proceed or abstain. If the action becomes facilitated after Istikhara, then it is good, even if one's chest does not feel expanded. It is advised not to marry except with complete contentment and thorough investigation, and that the foundation be religion and character.