Is it permissible for a person to give the Zakah (obligatory charity) to his daughter-in-law?
Yes, it is permissible for a person to give the Zakah to his daughter-in-law if she was poor, and wasn`t provided for sufficiently by whomever is obliged to provide for her. And Allah Knows Best.
Is it permissible for a woman who is in her `Iddah (waiting period) due to the death of her husband to go out and mix with non-Mahrams (Marriageable men)?
All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.
A woman in such a situation is only allowed to leave her house for a sound reason such as visiting the doctor, and she is only allowed to mix with her Mahrams (Non-Marriageable kin) since it is permissible for a woman, whether in her `Iddah, or not, to mix with her husband and Mahrams. However, she is allowed to accept condolences, and answer inquiries about her situation after such a calamity. And Allah Knows Best.
What is the ruling on the financial leasing transaction in commercial bank?
Any transation that is involved in the unlawful is impermissible. And Allah Knows Best.
Is it permissible to pay the Zakah (obligatory charity) for settling the debt of a deceased relative?
It is impermissible to pay the Zakah for settling the debt of the deceased since Zakah is paid to eligible recipients who are alive. As for the debts of the deceased, they are to be settled from the estate before dividing it amongst the heirs, but if the deceased didn`t leave an estate, then it is desirable for his/her heirs to settle those debts if they can afford them. And Allah Knows Best.