Should I pick up the newspapers thrown at the street because they definitely contain sacred names?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
The Messenger of Allah (PBUH) says: "Be mindful of Allah and He will protect you." Part of this is protecting whatever contains the name of Allah. Therefore, if you see a paper containing Allah's name thrown in the street, then you should grab it and similar papers, then burn them in a clean place. Doing so is permissible because Othman (May Allah be pleased with him) has burnt copies of the Quran which didn`t match the main Mus-haf. However, you aren`t required to collect every paper in the street. And Allah The Almighty 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 stored articles of merchandise even if they were stacked in the merchant`s stores for years because this is the way Islam has countered monopoly.
Is it permissible for a woman to pluck her eyebrows, or to shave them and have a tattoo in their place?
It is forbidden for a woman to pluck her eyebrows, or to shave them and have a tattoo in their place since this is called (Nums), and the Prophet(PBUH) has cursed those who do it.
Is it permissible for a wife to leave her house without asking her husband?
It is impermissible for the wife to leave her house without asking her husband except for a sound reason.