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.
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.
Is it permissible for the guardian to give Sadaqa (voluntary charity) from the money of the orphans?
It is impermissible for the guardian to donate from the money of the orphans because he is entrusted with the safekeeping of that money, and is prohibited from donating it.
I am a woman, and my natural menstrual cycle lasts six days. In the evening, I perform the testimony (Tashahhud) for myself, and then I engage in sexual intercourse with my husband. After intercourse, I experience bleeding, either immediately or the next day. Is my intercourse with my husband during this time forbidden?
It seems that your menstrual cycle lasts seven days, not six. Therefore, you should wait until the bleeding stops, then perform ghusl and pray. And Allah Knows Best.