Is it permissible to slaughter one animal as a sacrifice and an Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth)?
It is impermissible to do so since each of them is slaughtered for a different reason.
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 it permissible for a woman to use a contraceptive without telling her husband although he wants to have as many children as possible and she can`t care for them?
All perfect praise be to Allah, the Lord of the Worlds, may His Blessings and Peace be upon our Prophet Mohammad and upon all his family and companions.
If the pregnancy is harmful to the woman, it is permissible for her to use a contraceptive; however, this has to be backed by a medical report from a God-fearing doctor. In addition, you had better inform your of what you are doing to avoid dispute. And Allah The Almighty Knows Best.
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.