Is it permissible for a woman in her waiting period (Iddah) after her husband's death to leave her house and mix with non-Mahrams?
It is not permissible for a woman in her waiting period (Iddah) after the death of her husband to leave her house except for a necessity, such as for medical treatment, nor is she allowed to mix with non-Mahrams. A woman is not permitted to mix with anyone other than her husband or Mahrams, whether she is in her waiting period or not. However, there is no harm in accepting condolences from those who visit and responding to their inquiries about her well-being. And Allah Knows Best.
Is Zakah (obligatory charity) due on the money saved for marriage?
Zakah is due on the money saved for marriage if it reached the Nissab (minimum amount liable for Zakah), and a whole lunar year had lapsed over possessing it.
What is the ruling on someone who doesn`t perform prayer?
All perfect praise be to Allah,The Lord of The Worlds Not performing prayer is a major sin, and one who doesn`t pray out of laziness is considered an oft-sinner ;whereas, the one who denies that it is mandatory is considered a disbeliever. And Allah Knows Best.
After I had prayed, I found a drop of menstrual blood and was unsure when that happened; what is the ruling on my prayer and fast?
All praise is due to Allah, peace and blessing be upon the Messenger of Allah.
Your prayer and fast are correct ,and you should not make up for them, and we ask Allah, The Almighty, to duely reward you for these acts of worship. Your menses start once you see blood because the situation remains as such unless there is certainty or predominant conjecture, as per the Fiqh maxim: "Certainty is not removed by doubt". And Allah Knows Best.