Does ill-gotten money hinder the answering of the Du`a (supplication) and the means of subsistence?
Sins hinder the answering of the Du`a, and deprive the sinner from means of subsistence; whereas, acts of obedience facilitate making a living. Allah, The Almighty, Says (What means) : "And for those who fear God, He (ever) prepares a way out. And He provides for him from (sources) he never could imagine." [At-Talaq/2-3].
What is the ruling on buying a car from someone for less than the market price, because they are in a hurry to travel and want to sell their belongings at a lower price due to their urgency?
Yes it is permissible; however, a Muslim shouldn't take advantage of other's difficult situations.
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.
Although engaged to be married, a man committed adultery with another woman. What is the ruling of Sharia on this?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
There is no sin on the woman to whom this man is engaged; however, he is considered a cheater and must receive the punishment prescribed in Sharia. And Allah The Almighty Knows Best.