Is it permissible for a woman to abort the fetus due to difficult health and social circumstances, and what is the ruling on that, and does it entail expiation?

It is not permissible to abort a pregnancy at any of its stages, except for a legitimate reason and within very narrow limits. The Council of Senior Scholars defines the permissible cases:

Before 40 days (first stage): Abortion is permissible if there is a legitimate interest or to avert harm. However, fear of upbringing, costs, the future, or having enough children does not permit abortion. 40-120 days (clot or chewed-like substance): Abortion is not permissible unless a reliable medical committee determines that the continuation of the pregnancy poses a danger to the mother's life, and after all other means have been exhausted. After 4 months (after the ensoulment): Abortion is not permissible unless reliable specialist doctors determine that the fetus's continued presence will cause the mother's death, and after all means to preserve its life have been exhausted.

Social circumstances (as mentioned in the question) do not permit abortion. As for health circumstances, abortion is permissible before ensoulment if a reliable medical source determines that the fetus's continued presence poses a danger or harm that the mother cannot endure. Abortion is forbidden by the consensus of Muslims.

Regarding blood money (diyah) and expiation (kaffarah), their rulings vary according to the age of the fetus and the reason for the abortion.