Is Iddah (waiting period) incumbent on an old woman whose husband had died?
Upon the death of the husband, Iddah is incumbent on the wife regardless of their age. And Allah Knows Best.
Does Istigfar (Asking Allah for forgiveness) between the first and the second part of Friday prayer`s sermon render the prayer invalid?
Talking during Friday prayer`s sermon is disliked, but there is no harm in offering Istigfar between the two parts of the sermon, and it doesn`t invalidate the prayer as it is actually from Sunnah. And Allah Knows Best.
Do certain vaginal discharges and incontinence of urine nullify ablution, and should underwear be changed?
A person afflicted with constant impurity due to urinary incontinence and vaginal discharges is obliged to make ablution for every obligatory prayer when its time is due, and after removing Najaasah (impurity), and wearing a clean diaper. He/she is obliged to pray immediately even if the impurity is being released, and he/she is obliged to remake ablution, and the aforementioned for every obligatory prayer.
Is a woman`s neck an Awrah (private part)?
All Perfect Praise is due to The Lord of The Worlds.
It is an Awrah, and it is forbidden for her to reveal it before non-Mahrams (Marriageable men). And Allah Knows Best.
