What is the ruling of Islamic law regarding falling in love with a girl and then leaving her, knowing that she loved me and suffered a psychological condition because of it, and am I sinful for that? And what is the way to convince parents to marry a girl of a lower status?

He who loves a girl must keep himself chaste and not fall into what Allah has forbidden with her. You have erred by confessing your love to her, as this invites temptation. The best remedy for those who love each other is marriage, and the criteria for it are religion and character. Material and social differences are not a legitimate impediment. To convince the family, turn to Allah with supplication and seek help from those close to you. If the family is convinced, then that is well and good. Otherwise, obedience to them takes precedence, unless you fear temptation for yourself. And if it is not decreed for you to marry her, then there is no sin upon you.