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.
Is it permissible for the woman who is observing Iddah after her husband`s death to sit with her daughter`s suitor, although their marriage contract hasn`t been concluded yet?
All perfect praise be to Allah the Lord of The Worlds. May His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
A suitor who hasn`t concluded the marriage contract isn`t a Mahram*, so he must be treated as such. And Allah The Almighty Knows Best.
* The period a woman must observe after the death of her husband or after a divorce, during which she may not marry another man.
* In Islam, a mahram is a member of one's family with whom marriage would be considered haram, concealment purdah, or concealment of the body with hijab, is not obligatory; and with whom, if he is an adult male, she may be escorted during a journey, although an escort may not be obligatory.
Is it permissible for the wife to give the Zakah (obligatory charity) of her money to her poor husband?
Yes, it is permissible for the wife to give from the Zakah of her money to her poor husband. 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.