Is abandoning a girl considered an injustice to her, and will God answer her prayers, and is it permissible to perform the Istikhara prayer to know if she is a righteous wife or if she should be left immediately, after having an illicit relationship with her and proposing to her family with the sole intention of winning her over?

You must abandon the forbidden relationship. If you see that your advice to her is beneficial, you may perform Istikhara and propose marriage to her, provided she becomes righteous, chaste, and a Muslim, while ensuring your promise is sincere. If she does not respond to righteousness, then distance yourself from her and do not keep her in suspense.