Re: How young have folks let their kid use an outboard on their own?
I think my daughters were about 12 when I turned them loose in a 13' whaler. Made them take the CG test first, and they were raised in boats (older boats that frequently had problems, in shallow uncharted tidal waters where you often got stuck withno one around to help you!). I also gave them lots of training, including "touch and go" to piers and pilings, retrieving overboard items (I throw stuff overboard randomly and make them go back and get it) and mechanical (secretly unhook the gas line and let them figure it out).
One thing about boys: they can be responsible 10 year olds, but they turn in to 14 year olds, and no matter how good they are, will become risk takers, or oblivious to risk. Add some distacting girls around and they lose all focus. It's just their brains. Don't believe me? think back....
My small boat had a pull start. I believe that until you are old (big) enough to pull it you shouldn't be driving--it's a physical test. Think of something similar for your key start boats. An infant can drive a boat that's running, but you need weight and strength to deal with docks, anchors, paddles, shove poles and break-downs.
They also have to be big enough to climb in the boat if they fall over.
Making your child care for the boat is essential. Discipline and responsibility are the keys to safe and skilled boating. There is value in scrubbing a deck. I started with that same whaler and a wooden sailboat I had to paint every year.