The purpose of the NCAA is not to keep kids from hitting their baby momma or stealing a CD. The purpose is to see to it that the institutions and athletes that agree to the NCAA rules follow those rules.
Chase bank can fire you for violating a work rule. They can't fire you for cheating on your wife. Two separate things man. The school can choose to sit you for any of the things you mention, but that has NOTHING to do with the NCAA or its rules, which address how the schools recruit and treat athletes so that no competitive advantage is gained by one school. Domestic violence does not give School "A" an advantage over School "B". School "A" allowing its players to make improper $$$ will give it an advantage over school "B".