Is a woman`s prayer considered invalid if non-Mahrams (marriageable men) saw her offering it?
A woman`s prayer isn`t invalidated if non-Mahrams saw her offering it, but she had better pray in isolation.
Does passing wind, from the anus without a smell, invalidate prayer?
If a person is certain of having passed wind even if it was with no smell, then both his/her ablution and prayer are invalidated, thus he/she should remake ablution and re-perform prayer.
A man has married a second wife and deprived the first from provision and overnight stay. He spent most of his time and wealth on his second wife. After sometime, the latter got sick and was diagnosed with breast cancer, which made him forsake her in bed and return to his first wife. What is the position of Sharia on this?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
It is forbidden for a woman to forsake her husband in bed without a lawful excuse since this is one of the mutual rights of spouses. When the wife abstains from making love to her husband without a lawful excuse, she is considered sinful. This is because the Prophet (PBUH) said: "If a woman spends the night deserting her husband's bed (does not sleep with him), then the angels send their curses on her till she comes back (to her husband)." [Agreed upon]. And Allah The Almighty Knows Best.
Is it permissible to openly announce the engagement of a woman who is in her waiting period (iddah)?
It is not permissible to openly announce the engagement of a woman in her waiting period (Iddah), but it is permissible to hint (imply) at it if she is in her waiting period after the death of her husband. And Allah Knows Best.