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.
Is it permissible for a wife to leave her house without asking her husband?
It is impermissible for the wife to leave her house without asking her husband except for a sound reason.
Is it permissible for a woman who is in her confinement to fast upon seeing blood signs that are neither black, nor red ?
Brownish, reddish, and yellowish discharges are all considered confinement until there is no colored discharge which marks the end of confinement. Moreover, the aforesaid woman is prohibited from fasting until she attains ritual purity. And Allah Knows Best.
Should nail polish be removed before making ablution?
Yes, it should be removed because it prevents water from reaching the nails.