Towards your second topic:
I´m studying law and I can assure you, a contract is necessary to sell him. You can´t sell a player because you don´t own him, no matter if he plays in your youth team or not. It is actually the contract you are selling. The other club pays for the benefits you would have gotten from the contract. No contract, no selling.
But actually it would´t hurt to be able to sign more players for your team, as there is no such limit in real football. This would solve the problem as well.