What is the ruling on a man leading his sisters in obligatory prayer, or Taraweeh prayer (Night prayer in Ramadan)?
The prayer of the man who leads his wife, or sisters in prayer is valid, but it is more rewarding for him to offer obligatory prayer in the mosque. 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.
Is the marriage contract considered valid if concluded at home by the marriage official (Ma`zon)?
Yes, it is valid as long as it is registered at the court.
Should water be put in the deceased`s mouth and nose while washing him/her?
Putting water in the mouth and nose of the deceased while washing him is impermissible.