Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
Is it permissible for a woman to adorn herself with kohl (eyeliner) and go out wearing it?
Kohl is a form of adornment, and it is forbidden for a woman to display her adornment to anyone other than her husband or a Mahram. And Allah Knows Best.
What is the Islamic ruling on adoption, and what is the legal window through which a person can be kind to an orphan girl, attend to her needs and raise her as his own?
Kindness to an orphan entails a great reward from Allah, but adoption is prohibited and invalid. Therefore, it is permissible for the aforementioned person (for example) to make his brother`s wife breastfeed that girl so that he becomes her uncle by suckling provided that he informs her that she isn`t his biological daughter.
I`m a cashier at a branch of the Civil Service Consumer Corporation. Sometimes, customers pay more than the due amount. Do I have the right to take that extra money knowing that I cover shortages from my own salary?
All perfect praise be to Allah the Lord of the Worlds. May Allah`s peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
If customers give that money willingly to help you with the potential loss then this is permissible. And Allah The Almighty Knows Best.