Is vomit among the nullifiers of Wudu (ablution)?

Vomit does not nullify Wudu, but it is a Najaasah (impurity) that requires rinsing the mouth and washing whatever became dirty by it since the prayer becomes valid only after the removal of Najaasah. And Allah Knows Best.

What`s the ruling on using the following materials in manufacturing cosmetics: olive oil, Vaseline, talc powder, glycerin, honey, almond oil, pine oil, galingale and marjoram?

All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.                                                                                                                                                                                                                                    None of the above materials is forbidden, and it`s lawful to use them in manufacturing products that are beneficial to people. This is because, in principle, all things are lawful so long as there is no evidence in Sharia indicating otherwise. And Allah Knows Best.

Is it permissible to give Zakah (obligatory charity) to one`s poor sister, or brother?

It is permissible for one to give the Zakah to his poor sister, or brother if providing for them isn`t due on him, and the sister doesn`t receive sufficient provision from whomever that is due on. And Allah Knows Best.

My father passed away before my grandfather. Am I entitled to any share of my grandfather`s inheritance?