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.

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.

What is the expiation for breaking fast due to being on a journey, or being sick, or being in a state of menstruation?

No expiation is due on the aforesaid categories, but they are obliged to make up for the missed fast. However, if any of them failed to do so while being able to, and the next Ramadhaan has come, then making up for those days is incumbent on him/her , and paying the ransom as well. And Allah Knows Best.

Is Zakah (obligatory charity) due on articles of merchandise even if they were stacked in the merchant`s stores for years?

Yes, Zakah is due on goods even if they were stacked in merchant`s stores for years, in this manner Islam struggle against monopoly.