Has Islam made it incumbent on us to give our children particular names?
No, it hasn`t, but it is desirable that we give them good names.
Is Zakah(obligatory charity) due on the equipments 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.
Is Zakah(obligatory charity)due on an indebted merchant?
Debt doesn`t abrogate the dueness of Zakah, thus a debtor who has money, articles of merchandise, or other Zakah funds at his disposal should pay Zakah from 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.