Is it permissible for the children of a deceased father to settle his debt from the Zakah (obligatory charity) money due on them?
It is impermissible to use the Zakah of one`s money for settling the debts of the deceased. However, children should settle the debts of their deceased parents out of filial piety. And Allah Knows Best.
Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.
Should one obey his mother even if she was wrong?
Obeying one`s mother is an obligation in matters that are beneficial to her and so long as she didn't drive her children to commit an act of sin.
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.