About the topic mentioned in the question, our maraje’ have fatwas that are good to be mentioned here:
Question 1260: Is it permissible to practice abortion due to financial problems?
Answer: Mere financial problems don’t make abortion permissible.
Question 1261: After inspecting the mother in her early months of pregnancy, the doctor says that continuing with pregnancy can be life threatening to her and that there are also chances of the baby being born with defects and deformation, thus recommending abortion. Is this permissible? Is it permissible to abort a baby before its spirit has been breathed into it?
Answer: Deformation of the fetus isn't enough to make abortion permissible before its spirit has been breathed into it, but if a trusted doctor with expertise says that it threatens the life of the mother, it is permissible before its spirit has been breathed into it.
Question 1262: Using new methods and instruments, practitioners today can learn if the fetus has defects or not. Considering the hardships these children will face in their lives, is it permissible to abort babies that have been diagnosed with such by experts?
Answer: Aborting the baby just because it has defects or will face hardship in the future doesn’t make it permissible at any time. 
Issue 2453: It is impermissible for a woman who has been impregnated through illegitimate intercourse to abort her baby.
Khu’i, Araki, Golpaygani, Safi: If a woman is impregnated through illegitimate intercourse, in the case of her or the father or both being Muslim, she cannot abort her baby.
Makarem: A woman who has become pregnant through illegitimate means cannot abort the baby and it is considered her child, the only thing is that it won't inherit from her.
Sistani: Abortion is impermissible, even if the baby is illegitimate, unless keeping it has an unbearable harm or severe hardship for the mother, which in this case it is permissible to abort the baby before its spirit has been breathed into it but it will entail diyah (blood money), but after spirit has been breathed into it, it is in no way permissible. 
Ayatullah Mahdi Hadavi Tehrani’s viewpoint in this regard is:
If keeping the baby has a considerable harm for the mother or entails severe difficulty and hardship for her, abortion is permissible before spirit has been breathed into it and as long as one isn't sure of the harm or difficulty, and there aren't considerable chances of such happening either, it will remain haram.
In order to have been cautious, it is wajib to refer to the qualified judicial authorities and to get verification from expert practitioners before doing so.