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.
Should the father command his ten-year-old daughter to wear the Islamic dress?
All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.
The father should order his daughter to put on the Islamic dress once she turns ten, in order for her to get used to it. 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.
A man break his fast once during Ramadan and he already have an expiation of fasting for two consecutive months. He fasted for a month and passed away. Is it permissible for his sons to fast the remaining month equally?
Fasting for expiation must be performed consecutively. I advise his children to feed sixty poor people, giving each one half a kilogram of rice or its monetary equivalent. This is because if a living person is unable to fast, they are required to feed sixty poor people, and death constitutes an inability. And Allah The Almighty Knows Best.