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.

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 go to the bathroom wearing a necklace that has the word "Allah" inscribed on it?

All Perfect Praie be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.

Anything that contains words pertaining to Allah, The Almighty, is desired to be left outside when going to the bathroom, or to be hidden for fear of losing it. And Allah Knows Best.

Does the clipping of nails nullify ablution?

No, it does not, and it is preferable to wash the hands afterwards.