Does passing wind, from the anus without a smell, invalidate prayer?

If a person is certain of having passed wind even if it was with no smell, then both his/her ablution and prayer are invalidated, thus he/she should remake ablution and re-perform prayer.

I have concluded my marriage contract at a Sharia court; however, one day I was talking to my fiancée over the phone and she got on my nerves leading me to utter one divorce. This is knowing that I can`t tell my her father because he is very strict and will not accept that at all. What is the best course of action that I should pursue in this situation?

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.

Does offering Udhiyah (Offering a Sacrificial animal at Aid Al-Adha) avails from offering Aqiqa?

Offering an Udhiyah doesn't avail a person from offering Aqiqa because each of which is a different act of worship. And Allah Knows Best.