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.

Should one fulfill his vow of donating an animal to the poor and needy with one sheep although he had repeated the vow several times?

Each vow has to be fulfilled, and repeating the words of the same vow for confirmation renders its fulfillment obligatory as one vow. As for multiple vows, they have to be fulfilled as well.

Is Zakah (obligatory charity) due on the items used in the trading process such as: cars , shops etc..?

No Zakah is due on equipments used in the trading process such as cars and the like.

Is it allowed for me to donate a flat to each of my children except one considering that the tuition fees I paid for the latter`s university study are equal to the price of the flat? In other words, he has received his share and this is why I`m donating a flat to my other children?