How can one deal with a fiancé who talks about sex and shows signs of stinginess, with concerns about his lineage and his future influence on children, especially since the family is not convinced by him and refuses to annul the engagement?

The preponderant opinion is that the relevant compatibility is in religion and character. A suitor should not be rejected merely because of his lineage, unless the woman or her children fear disgrace. A woman has the right to break off an engagement even without a reason, or if there are undesirable qualities. It is advised to take time and perform Istikhara (prayer for guidance). If she decides to break off the engagement, there is no sin upon her, even if her parents object, as they have no right to compel her to marry someone she does not desire. It is important to note that a suitor is a stranger to his fiancée, and they are not permitted to speak except within Sharia (definition)-compliant guidelines and to the extent of necessity. Speaking about conjugal relations is forbidden.