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 is the ruling on shaving the head of the newborn?

It is desirable to shave the head of the newborn on the seventh day from delivery, and the weight of his/her hair is given in gold , or silver as charity.

Is Making up Missed Obligatory Prayers an Obligation? 

Is it permissible for a woman who broke fasting due to a delivery to pay a ransom?

She should make up for the missed fasting days once she becomes ritually pure, but it is impermissible for her to pay a ransom while being able to fast.