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.
If a father stops his daughter from getting married, is it permissible for her to conclude the marriage contract herself?
It is permissible for the father to stop his daughter from getting married if there was a lawful reason for that, and she isn`t allowed to conclude the marriage contract without her guardian. However, if her father denied her right in getting married for an unlawful reason, then she should go to court.
What is the ruling on making a false oath?
Making false oath indulges its maker in Hell; therefore, he is obliged to repent, ask Allah for forgiveness and make an expiation; feeding 10 poor or providing clothes for them and in case of incapability of doing any of latters he should fast for 3 consecutive days. And Allah Knows Best.
What is the ruling of Sharia on woman shaking hands with non-Mahram man?
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) said: "It is better to be stabbed in the head than touch a woman to whom one isn`t related." [Transmitted by Al-Tabarani /Al-Mo`jam Al-Kabir, Hadith No.16880]. Accordingly, it is forbidden for men to shake hands with non-Mahram* woman. And Allah The Almighty Knows Best.
* The women/men that you are allowed to marry. It includes all women/men other than mahram (including cousins).