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.
What is the ruling on giving Zakat al-Fitr in cash?
The default ruling is that Zakat al-Fitr should be given as the staple food of the land. In Jordan, for example, the staple food is wheat or rice, and the amount of Zakat al-Fitr is 2,500 grams per person. It is easy to give this amount of rice to the poor and needy, and this is the correct ruling according to all Islamic schools of thought.
However, Hanafi scholars have permitted giving Zakat al-Fitr as monetary value, considering it more beneficial for the poor and easier for the giver.
Is it permissible for a pious Muslim woman to stay with her husband who had quit praying out of laziness?
Quitting prayer is one of the major grave sins that come after disbelieving in Allah, but the wife of such a person isn`t considered divorced, rather, she should exert all her efforts in order to bring him back to the way of Islam. However, if his sin is likely to lure her from the way of Islam, then she had better separate from him by lawful means such as Mokhal`aa (When a wife pays a compensation for her husband in return for divorcing her). Moreover, if she exercises patience, and remains steadfast on her faith, then there is no harm in doing that.
Is it permissible for one to give the Zakah (obligatory charity) to his indebted brother?
It is permissible for one to give the Zakah to his brother if he was indebted, or poor.