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.
How many Rak`ahs (unit of prayer) are offered in Witr prayer?
All perfect praise be to Allah, The Lord of The Worlds Witr (an odd number prayer performed between Isha`a and Fajr) is offered with a minimum of one Rak`ah, and a maximum of eleven, but offering three Rak`ahs is the minimum of its complete form. And Allah Knows Best.
Is the prayer of a woman who is led by an Imam via T.V. permissible?
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. Amongst the conditions for the validity of prayer is that both the Imam and those led by him must be in the same place. Thus, the prayer of the person who is being led by a televised Imam is invalid unless he/she was with him in the same mosque. And Allah Knows Best.
I have mixed (halal and haram) money, and I want to purify it. My father is poor, and I want him, my mother, and my mother-in-law to perform Hajj, along with myself and my wife, as they need care due to their old age. Is it permissible to use this money for Hajj, or what should I do with it? Please advise.
If you knew the exact amount of unlawful money, then you should give as a charity, and if didn't then try to figure out the closest amount in order to give it as a charity.
As for performing Hajj, perform it by using your lawful money. May Allah Bless you for being dutiful to your parents and your mother in law and for your attempt to serve them, And Allah Knows Best.