Is the questioner obligated to marry a girl with whom he had an illicit relationship, then he discovered the wickedness of her family and doubted her past sexual practices, or should he leave her?

You erred by establishing a relationship with a girl who is unlawful for you, and she demands forbidden things from you, thus violating the words of Allah Almighty: "Tell the believing men to reduce [some] of their vision and guard their private parts," and the words of the Prophet, peace and blessings be upon him: "No man is alone with a woman but the third of them is Satan."

You must repent and sever your ties with her. Your marriage to her is not good for you, because she is not religious and it seems she comes from a bad environment. The Prophet, peace and blessings be upon him, said: "So marry the one who is religious, you will succeed."

Distance yourself from her completely, and you have no obligation towards her. If you wish to help her, suffice it by inviting her to repentance through your sisters or female mahrams. If she repents and her condition improves, then there is no objection to your marrying her.