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.
Is permissible to buy/sell with non-Muslim?
Yes buying/selling for a Muslim with non-Muslim is permissible as regards what is lawful.
What is Aqeeqah?
It is the sheep slaughtered on the seventh day from the child`s birth, and it is a confirmed Sunnah after the Prophet (PBUH).
Is Zakah (obligatory charity) due on the Zakah money received by a poor person, and reached a Nissab (minimum amount liable for Zakah), and a whole lunar year had lapsed over having it in his possession?
Yes, the poor who possessed a Nissab for a whole lunar year is obliged to pay the Zakah due on that money even if it was given to him as a Zakah money in the first place. And Allah Knows Best.