Is washing the private part after urinating (Istinjaa`) a condition, and is it done with water and soap, or with water only?
Istinjaa` is obligatory for removing impurity, and it can be done with toilet paper, or a stone, or water. It is preferable to do Istinjaa` first with paper, or stone, or the like, then to wash the private part with water until making sure that the impurity has been removed. Using soap is not a condition, but there is no harm in doing so provided that it is washed off with water. It is also permissible to use either water, or paper if impurity is removed by any.
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.
Is it allowed for me to donate a flat to each of my children except one considering that the tuition fees I paid for the latter`s university study are equal to the price of the flat? In other words, he has received his share and this is why I`m donating a flat to my other children?
All perfect praise be to Allah the Lord of the Worlds. May Allah`s peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Yes, it is permissible because you want to treat them justly. And Allah The Almighty Knows Best.
What should one who forgot to offer the second Sajda during congregational prayer, and remembered it before the end of the prayer do?
All perfect praise be to Allah, The Lord of The Worlds. Whoever forgets a pillar of prayer while in congregation must follow the lead of the Imam, and after the latter offers Tasleem, he should offer one Rakah, then perform Sujood As-Sahw (prostration of forgetfulness). And Allah Knows Best.