What should a girl do after learning that her current parents are her adoptive parents, and that her real mother, who bore her, has appeared and wants to prove her lineage from a man who deceived and abandoned her, knowing that she carries the lineage of her adoptive parents?

You must correct your lineage, as attributing oneself to other than one's biological parents is a grave sin. You must formally amend your lineage, or at least inform your relatives of the truth of your lineage to avoid genealogical mix-ups. If the biological father acknowledges you, you may attribute yourself to him; otherwise, you can attribute yourself to a name indicating servitude to God, such as "Bint Abdullah" (Daughter of the Servant of Allah). If your adoptive mother breastfed you five times before the age of two, she is your mother by suckling and one of your mahrams (unmarriageable kin); otherwise, you must observe hijab in front of the adoptive father, and you must maintain a relationship of kindness and dutifulness with that family.