Is it permissible to abort a less than one-month-old fetus?

What is the ruling on swearing on the Holy Quran and breaking that oath?

It is impermissible to swear on the Holy Quran in vain, and it is also impermissible to subject it to such an act since breaking the oath after swearing on the Quran entails an expiation.

Is it permissible for a woman to inherit the same share as of a man?

All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all if his family and companions.                                                                                                                                                                                                 Thorough studies in which woman's right to inherit according to law of distribution of estate indicates that there are more than one case by which women inherit the same as man and sometimes much more, or to shed the lights regarding the right to inherit while men who share the same family line with her don't have the right to inherit because the deceased has closer ties of kinship with her. In addition to four cases whereas woman inherits half share in comparison with man's share although they had the same degree of kinship with the deceased. For further details as regards the latter cases, kindly refer to elaborated jurisprudence books. And Allah Knows Best.

What should a worshiper who has forgotten a pillar of prayer do?

If he/she remembered the forgotten pillar before offering it in the following Rakah (unit of prayer), then he/she should offer it, and continue the prayer, then offer Sujood As-Sahw (Prostration of forgetfulness) at the end of it. But, if he/she remembered that forgotten pillar after having offered it in the following Rakah, then he/she should offer a new Rakah in its (the one in which he forgot a pillar) place, and offer Sujood As-Sahw.