What are the obligations of the inquirer toward the child and its mother, what is the punishment for him if he harms or aborts the child, and is he permitted to continue inviting to Allah despite his sins?

You went through a difficult period, and Satan was able to overpower you, but the most important thing now is to correct your repentance to Allah from disbelief and apostasy, and to abandon sins. Indeed, calling to Allah, enjoining good, and forbidding evil are signs of sincere repentance. Strive in calling to Allah, and try to leave the shelters that cause fitna. If you repent with sincere repentance, then you are not responsible for anything concerning this girl except inviting her to repent, while being cautious of fitna. And if it is possible for this to be done through another woman, it is better. Inform her of the sanctity of abortion, and urge her to repent. If she keeps her child and has no money, then you and her child should help her with what you can. Be cautious of her fitna if she does not respond, and be certain that your salvation lies in sincere repentance from the past, reforming the future, and getting married to protect yourself.