Did I wrong the girl I wish to marry, and should I apologize to her, after I advised her regarding her question about how to tighten the abdomen and enlarge the buttocks via Facebook, knowing that she does not reciprocate my feelings, so should I give up on her? And what should I do now?

It is not permissible to chat with a girl via social media under the pretext of studying. What is obligatory is repentance and severing all ties with her completely. Searching her accounts is a curiosity that does not concern you, and "part of a person's good Islam is his leaving alone what does not concern him." What is published on Facebook is available to everyone, and what you did is not an attempt to trace her missteps, but rather you must cut off all ties with her.