Is it permissible for the man to go out wearing shorts?
It is permissible as long as his Awrah(private part), which is between his navel and knee, is covered. However, the regular wear traditions and modesty are to be observed.
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 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 one to shake hands with his uncle`s daughter?
No, it isn`t because he is a non-Mahram(Marriageable) to her.