Solved

Young drivers. Earn money?

No, IMO you'll never recoup your costs.

Yes, you get a T20 driver from your youth academy and train them for your own use because their wages will be very low in comparison to one you would buy from the market. They start at a little over over £300k per race. So this is the best and most cost effective way to get a good driver for your own team.

Training a driver to a high level then trying to sell is a recipe to lose money. First of all it takes 15 tokens and some game cash (edit... no game cash) to promote from your academy. Then it takes a while to train them and all of the time they're drawing £300k+ per race wages. Then when you do try to sell them at auction nobody buys. The reason is that only L18+ managers are allowed to buy them and with a wage bill of £1.2m per race most high level managers would prefer to use their own academy drivers.

If you're feeling kind and want to help out a newbie who is keen to continue playing iGP after the novelty wears off, you can promote a T20 driver from your academy and pass them on to the newbie without training. This keeps the wages low for the new manager and it will only cost them 3 tokens and a couple of million game cash to hire the driver.
Warning: Be careful with training, go too far and the driver level may increase too much for the newbie to hire. It also pushes up the purchase price and wages.
So if you're doing this to help out a rookie you either don't train at all or just train "Physical" to 20 Stamina and minimum weight. The reason for this is that as a high level manager it doesn't take you very long to get "Physical" maxed out and it also doesn't push the driver level or wages too high.