What is the ruling on buying a car from someone for less than the market price, because they are in a hurry to travel and want to sell their belongings at a lower price due to their urgency?
Yes it is permissible; however, a Muslim shouldn't take advantage of other's difficult situations.
What is the ruling on a vowed animal sacrifice?
A vowed animal sacrifice is to be distributed amongst the poor and needy, and neither the vow-maker, nor those supported by him are to eat from it.
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 for a person who had vowed to give a certain amount of money to another, but didn`t find the latter to donate that money to the mosque?
In principle, the vowing person should abide by his vow as much as possible. Therefore, if he couldn`t find the person that he had made the vow for, then the vow itself is countless and nothing is due on its maker. However, if the latter happens to find the former later on then, he has to give him that money.