What is the ruling on abortion in this case, and what is the solution and advice offered to the woman?

The questioner must first repent to Allah, for establishing an illicit relationship with a Christian man, committing adultery, and then desiring an abortion are considered grave sins. Adultery with a non-Muslim is even more reprehensible and indicates a flaw in one's creed, which forbids befriending and aligning with disbelievers, as stated in the verses: (You will not find a people who believe in Allah and the Last Day loving those who oppose Allah and His Messenger) Al-Mujadilah/22, and (O you who have believed, do not take the Jews and the Christians as allies) Al-Ma'idah/51, and (O you who have believed, do not take My enemies and your enemies as allies) Al-Mumtahinah/1.

The conditions for repentance are: regret, ceasing the sin (by ending the relationship with this man and others), and resolving never to return to the disobedience. The completeness of repentance includes steadfastness, striving in acts of worship, and giving charity, as stated in (And indeed, I am the Forgiver of whoever repents, believes, and does righteousness, and then is guided) Taha/82. Repentance opens the doors to relief, as in (And whoever fears Allah - He will make for him a way out) Al-Talaq/2, while turning away from the remembrance of Allah brings a life of hardship, as in (And whoever turns away from My remembrance - indeed, he will have a difficult life) Taha/82.