Is the son of the sister by breastfeeding considered a mahram in Islam, and is it permissible for a woman to go for Hajj with him?
Everything that is prohibited by lineage is also prohibited by breastfeeding. The son of the sister by breastfeeding is considered a mahram, just like the son of the sister by blood, and it is permissible for him to be her mahram for Hajj and Umrah. And Allah Knows Best.
Is it true that whatever is dry is pure even if there was impurity on it?
The impure material object does not soil (make impure) anything else unless the impurity is wet and transferable. But, if the impurity is dry or non-transferable, then there is no problem. Fuqaha has stated that: There is no disagreement between Muslim scholars that when a dry impurity touches something dry it does not make the latter impure.
My father placed shares worth twenty dinars in one of the banks, and their value doubled to become five thousand dinars. When my father passed away, one of the scholars told us that it is permissible for us to take the money. What is the ruling on this money, considering that it comes from a bank and involves interest (Riba)?
Allah The Almighty Said (What means): "And if you repent, then for you is the principal of your wealth. You do not wrong, nor are you wronged." [Al-Baqarah/279]. This is the precautionary ruling regarding what you are asking about. You are entitled to the principal amount, and you should give the excess as charity to the poor and needy. If you are poor, you may take from it. And Allah The Almighty Knows Best.
Is the patient who is on dialysis twice a week obliged to observe fasting? Is his fasting on the days he is on dialysis considered valid or not?
Praise be to Allah the Lord of the Worlds.
Dialysis invalidates fasting because of the nutritional fluid used in that procedure, as pointed by specialized doctors, in addition to causing bodies to enter the stomach. Therefore, it is recommended that the patient who had undergone dialysis to observe fasting for the rest of that day, if he is able to, and make up for it after Ramadan. However, if the doctor told him that fasting, at any time, would damage his health, then he must break his fast and pay a ransom against every missed day. We pray that Allah blesses this person with recovery. And Allah The Almighty Knows Best.