Who is required to fast?

Any adult, sane, and hardship enduring Muslim person is required to fast unless there were prohibiting conditions such as menstruation and confinement.

How to pay Zakah(obligatory charity) on articles of merchandise?

Articles of merchandise are estimated by their whole sale market price at the end of each lunar year, and (2.5%) of their value is paid as Zakah whether it(value) went up, or down compared to actual purchasing price, and whether the increase(profit) was in the article itself such as an increase in the animal`s weight, or in the prices themselves.

Is it permissible for a Muslim to escort his deceased disbelieving relative to his final resting place?

It is permissible provided that he doesn`t walk behind non-Islamic symbols, rather he should walk in front of them.

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.