In general Islamically speaking, we are not accountable for the actions of others unless we have a clear and direct role in it.
So to answer the questions about haram income of parents, there is no sin on the children taking money or having it spend on them. It is the parents' problem, not the child.
https://islamqa.info/en/answers/215/a-minor-whose-parents-income-is-haraam
In fact, it's even ok to inherit wealth that was earned from haram sources. Obviously as long as once you have inherited you make sure the money is no longer involved in any impermissible investments and what not.
For your 4th question, again you are not accountable for actions of others. So let's say I teach someone a skill, like I teach someone how to drive and get their license. Then they go on go become a delivery driver for an alcohol company. It's not on me if all I did was teach them how to drive (unless I taught them knowing they were trying to become an alcohol delivery driver). Or if for example I sell someone my car, without knowing what they are going to use it for, and then they use it for delivering alcohol. It's not sin on me as there's nothing wrong with selling my car, can't control what the person does with it and it's not my problem anymore.