Is it permissible for a woman to apply Kuhul(Halal eyeliner) and go out wearing it?

Kuhul is part of a woman`s adornment, and it is forbidden for her to show that to anyone other than a husband , or a Mahram(Unmarriageable kin).

What is the ruling on swearing a false oath by the Holy Quran?

Swearing a false oath by the Holy Quran dips the oath-taker in Hellfire, and one who had done so should turn to Allah in repentance, seek His forgiveness, give back rights to whom they belong, and pay the oath expiation.

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 Aqeeqah due on the miscarried embryo?

No Aqeeqah is due on the dead embryo.