I know people who are 45 and have never had a job and just been taken care of by their parents their whole lives. If their parents were gone, they would not survive. Because they are a child who can't take care of themselves.
The cause and effect are backwards in most of the scenarios you provided though. Living with your parents doesn't mean you can't take care of yourself, but not being able to take care of yourself means you need to live with your parents. So yes, when you see an adult child, they almost 100% of the time live with their parents, but that doesn't mean all people living with their parents are adult children. To me, "child" reflects your ability to take care of yourself, not where you live.
You have a job and pay for things yourself. That's not a child. There may be other complications in your situation, and I'm not going to say everything is perfect, but it sounds like "incapable child" isn't specifically one of the problems.

