Is a girl of unknown parentage held accountable for her unwillingness to communicate with her biological mother, whom she found after a long search, and for her refusal to live with her or to love her and her children?

You must honor your mother and be good to her. The mother's right is great and does not diminish, even if she is a disbeliever or if you were born out of wedlock, for being born out of wedlock does not negate motherhood. You must suppress any feelings of hatred you find towards her and force yourself to treat her with kindness.

As for her request for you to stay with her, it appears obligatory to obey her in this, because obedience to parents is obligatory in permissible matters, even if difficult, so long as it does not result in severe harm. If her request is definitive and contains benefit for both her and you, then you must obey her.

However, if your staying with her will cause you harm, then you are not obliged to obey her at that point, and you can apologize to her in a way that pleases her. It is permissible for an adult, mature, trustworthy woman to live alone if the place is safe, but this is difficult to ascertain in this era.