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)?

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.

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.

Should vowed fast be offered in consecutive days, or not?

Vowed fast should be offered in line with what was originally intended by the vow-maker, either consecutively, or not.

What is the ruling on someone who vowed to fast for two consecutive months, but failed to do so?

He is obliged to fulfill his vow by fasting for two consecutive months, but if he fails to do so then, it remains a debt on him until he either fulfills his vow, or dies. In case of his death, his guardian is supposed to fast on his behalf, or donate food from his estate in return for fasting, but if the guardian fails to do so then, it is all in the Hands of Allah.