In management sims, I usually like to create myself as a teen and watch my career develop. Is that possible in this game

Yes in the commissioner office there is the option to add a player to the league and you can edit him to have whatever ratings you want or you could edit one of the players in the draft class in the same way if you want your player to be drafted.

How can we edit the players in the draft class? They don't appear in the add/edit player screen in the comissioners office.

They should appear in the commissioner office edit screen once they are actually in the game (so just prior to the draft) but not while they are just on the prospect list for the next draft.